Nice little idea you have here!
I like how you don't need to take a trip directly to the inn and can take it one step at a time. It's a mechanic that could really be expanded upon with some work. For instance, you may give players some kind of bonus for taking fewer separate trips to arrive, and punish those who take too long (also because, as it is, the mechanic can be exploited for infinite viewing time without risks). You could also add another bonus for taking the shortest route possible...
Only thing that feels a little odd is the way you lose oxes, which seems to be rng most of the time. I don't think it works too well right now.
Anyway, with work and polish this game can become quite a precious gem!