Dream has bigger problems than just Tiny Hut
All spells require A Clear Path to the Target
To target something, you must have a clear path to it, so it can’t be behind total cover.
So, while the range is theoretically unlimited, it has a very hard practical limitation that there must be an unobstructed straight line between the caster (not the sender who might not be the caster) and the target. So, if they sleep in a bedroom, or a tent, or a Tiny Hut, or behind a hill, or over the horizon, they are ineligible targets.
Now, you can mount an argument that that isn’t the intent of the spell and that limitation is a serious, possibly fatal, nerf to a 5th level spell. That’s an argument I’m sympathetic to but it isn’t one supported by RAW.
The designers could have solved the problem by making the target the sender, rather than the recipient, of the Dream but the text is crystal clear that the Dream recipient is the target. The could have also explicitly overridden the clear path requirement but they didn’t.
As such, the Tiny Hut in combination with the ground it rests on will stop Dream.
However, if you DM rules that Dream doesn’t require a clear path then, while the Tiny Hut blocks it, the ground doesn’t.