This is a classic "rulings, not rules" situation. Where you can and can't put a LTH is up to your DM.
I like to use the "Which ruling can be abused the most - don't take that viewpoint" approach.
If LTH is immobile with respect to things like ships, a wizard could destroy the strongest ship ever built by teleporting into the hold, casting LTH, and then teleporting back out, if there was a strong wind and the ship was under sail.
If LTH is mobile with respect to things like wagons, then armies would use them as tanks.
Therefore, neither of those things work, because it's magic and it doesn't have to make sense. A LTH on the deck of a ship moves with the ship, a LTH on a large wagon slides off. Perhaps the weight of the thing carrying the LTH has to be at least 10 tons. If you can tame a 10-ton dragon, you're probably past the point where LTH is a big advantage in combat anyway.
Also, it's a plausible ruling that the things that were within LTH when it was cast (other than the caster) cannot be separated into two things, one inside the hut and one outside - so firing arrows from within LTH won't work. The archer has to step outside, fire, and then step back inside.
LTH can be used to block narrow passes, or narrow straits. To cast underwater you need Water Breathing in some form, but if cast in a passage only 10' wide, or in water not much greater than 10' deep, it's a nice plug.