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Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faerzress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki

I would say that...

Depending on how the DM wants to rule it, they could say that the Faerzress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faerzress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faerzress, so the players would not suffer from madness

This question asking Can a dragon's breath weapon pass through Leomund's Tiny Hut? also provides a similar answer, and a good point in that:

The Hut aims to provide a safe space to rest, where the players can't be attacked from the outside. This ruling makes no sense in that context, and is (in my opinion) just the result of a poorly-worded spell.

Allowing A to penetrate the Leomund's Tiny Hut would make it more difficult for players to find safe places to rest.

Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faerzress is described as being: "An unusual magical energy" (Out of the Abyss: Page 21) and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki.

I would say that...

Depending on how the DM wants to rule it, they could say that the Faerzress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faerzress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faerzress, so the players would not suffer from madness

This question asking Can a dragon's breath weapon pass through Leomund's Tiny Hut? also provides a similar answer, and a good point in that:

The Hut aims to provide a safe space to rest, where the players can't be attacked from the outside. This ruling makes no sense in that context, and is (in my opinion) just the result of a poorly-worded spell.

Allowing A to penetrate the Leomund's Tiny Hut would make it more difficult for players to find safe places to rest.

Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faezress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki

I would say that...

Depending on how the DM wants to rule it, they could say that the Faezress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faezress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faezress, so the players would not suffer from madness

This question asking Can a dragon's breath weapon pass through Leomund's Tiny Hut? also provides a similar answer, and a good point in that:

The Hut aims to provide a safe space to rest, where the players can't be attacked from the outside. This ruling makes no sense in that context, and is (in my opinion) just the result of a poorly-worded spell.

Allowing A to penetrate the Leomund's Tiny Hut would make it more difficult for players to find safe places to rest.

Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faerzress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki

I would say that...

Depending on how the DM wants to rule it, they could say that the Faerzress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faerzress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faerzress, so the players would not suffer from madness

This question asking Can a dragon's breath weapon pass through Leomund's Tiny Hut? also provides a similar answer, and a good point in that:

The Hut aims to provide a safe space to rest, where the players can't be attacked from the outside. This ruling makes no sense in that context, and is (in my opinion) just the result of a poorly-worded spell.

Allowing A to penetrate the Leomund's Tiny Hut would make it more difficult for players to find safe places to rest.

Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faezress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki

I would say that...

Depending on how the DM wants to rule it, they could say that the Faezress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faezress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faezress, so the players would not suffer from madness

Probably Not

I've written this answer with spoilers as the original question included them. Possible tiny (pun intended) spoilers for Out of The Abyss.

Leomund's Tiny Hut states that:

Spells and other magical effects can’t extend through the dome or be cast through it

It would appear that A is magic, or at least magical.

Faezress is described as being: "An unusual magical energy" and that it "was in fact created by Elven High Magic" The Forgotten Realms Wiki

I would say that...

Depending on how the DM wants to rule it, they could say that the Faezress was already in the perimeter of the Leomund's Tiny Hut when it was cast. This could mean that they would be affected by madness.

Otherwise:

if the faezress was not already in the area that Leomund's Tiny Hut was cast, then it is likely that the tiny hut would not be penetrated by the faezress, so the players would not suffer from madness

This question asking Can a dragon's breath weapon pass through Leomund's Tiny Hut? also provides a similar answer, and a good point in that:

The Hut aims to provide a safe space to rest, where the players can't be attacked from the outside. This ruling makes no sense in that context, and is (in my opinion) just the result of a poorly-worded spell.

Allowing A to penetrate the Leomund's Tiny Hut would make it more difficult for players to find safe places to rest.