Tiny Hut blocks spells on creatures or objects inside the hut; but does not block spells on itself
To give a concrete example: If a spellcaster were to cast Dispel Magic on a creature that they knew was inside the dome, the spell would fail, regardless of whether they were physically capable of seeing their target or not (a circumstance that is contingent on, among other things, whether the inside were darkened or not, per the spell description).
But if that same spellcaster were to target the hut itself, the hut would be eliminated. There aren't rules in 5th edition that adjudicate the idea that Dispel Magic—or any other kind of abjuration magic—is required to "pass through" its target as part of the mechanism of affecting it; there's only the implied requirement that a spell must reach a target, passing through any obstacles between the caster and its target. As a result, a spellcaster casting such a spell would only have to make the spell "pass through" the hut if the spell specifically says that's what it does, which Dispel Magic does not.
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends. For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell's level. On a successful check, the spell ends.
—Dispel Magic, Player's Handbook, pg. 234