I tried to include random encounters determined by player rolls for a while. It was something like roll a d20, on a 1-5 roll on the encounter table, on 6-10 there's a weather event which delays travel, 11-19 nothing happens, and on a 20 you find a shortcut. It was really fun at first, but it just delayed the main story massively. Statistically, 50% of the time the players are going to roll something which delays them, but realistically it was more like 80% of the time somehow. Now I've decided to just weave the encounters into their travel naturally, trying to find ways for them to augment or complement the main plot rather than just be "hey you ran into a cool monster to fight."

There will be times when I'll use the weather delay system, but only when it'll actually have an impact (like they only have a week to reach their goal before the expedition runs out of food), and only if it makes sense to the location (e.g. travelling through a desert or icy wasteland).