What happens if you don’t finish quests?

I’m currently on the progression quest to unlock horses, but I don’t think I’ll finish it in time. What happens if you don’t finish a quest? Is the feature just never available for you or can you retry later on or something?

Note: I can’t progress because I have another building under construction and can’t build the stables. I don’t want to spend real $ on lp to finish the construction early.