It is primarily a matter of "Specific over General". The General rule is this (emphasis mine):
A typical spell requires you to pick one or more targets to be affected by the spell's magic. [...] To target something, you must have a clear path to it, so it can't be behind total cover.
The Range of a spell is strongly linked to what you can target. It's primary function is to restrict what you can target:
The target of a spell must be within the spell's range.
Now the Specific part: Dream has a Range of "Special", strongly suggesting that the typical (see emphasis above) rules for targeting do not apply. It also says:
Choose a creature known to you as the target of this spell. The target must be on the same plane of existence as you.
It is more than reasonable to assume that the majority of creatures on the same plane of existance as you do not have a clear path to them. Yet they are still valid targets. Spells do what they say they do, and this one allows you to pick as target a creature that you know on the same plane of existence as you. This is a Specific rule, which usually trumps the General rule.
Therefore, not being restricted by LOS rules, Dream is not affected by the rules of Tiny Hut that say:
Spells [...] can’t [...] be cast through [the dome].
No part of Dream is an effect that would have to travel in some sort of line through any part of the dome. Instead, the effect simply "materializes" in the target's dreams. Note: effects such as "blocking any spells cast into or out of the area" are present in other spells (Forcecage), but that is not what Tiny Hut says.
Bottom line: Yes, Dream can reach a target sleeping in Leomund's Tiny Hut.
But Message explicitly says "You can cast this spell through solid objects." Message has a Range of 120 ft and starts with "You point your finger toward a creature within range." Neither Dream, nor Scrying, nor Sending do either of those.
(I'll add more as they come in)