supply wagon - carries food, water, and extra gear in case you die and get looted. also acts as a mobile respawn point until destroyed. can only be destroyed by fire or catapult.
war wagon - carries all necisary tools and materials to build siege equipment. but at a limited supply. i.e. can build 2 catapults or 1 battering ram. interface could be right click and select siege equipment and poof now you have it. wagon is consumed on use.
cargo wagon - can carry anything else u wanna bring or can be left empty to fill with loot.
all these must be pulled by a tamed animal of course and all should only be able to be destroyed by fire or catapult shot. however they can be captured (stolen) if left unattended. and there should only be 1 supply wagon allowed active per tribe. and no more then 3 war wagons allowed per tribe with no limit to cargo wagon as they can be used for anything.
getting stuck wont happen. most likely theyd be restricted to more even terrain prolly similar to what u can walk over as they gotta allow for those that live in the mountains