You don't even have to quit the game. Log out of the character and log back in and the ride will resume (at least it has for me the last two times this happened).
I thought, one will be dismounted when logging out. If not, much better...
While playing on Gladden, I've experienced general lag problems and spikes that I don't experience on Elindilmir or Crickhollow. I've also experienced stable mount problems on Gladden.
Stable Mount Problems:
I'm not sure exactly when it all started, but for at least several days my stable mounts have been crashing into fences or just freezing during the journey. I'd say it probably happens during 33% of my journeys.
When they get caught in a fence the game won't let me logout, so a more drastic game exit is required. When I log back into the game, the mount continues the journey.
The other type of problem is when the stable mount freezes during the journey with no visible objects in its path. I have waited 11 minutes in the hope that it is a lag issue, but it isn't lag. I was able to dismount and continue playing (whereas a dismount is not possible when the mount gets stuck in an environmental object).
Had the problem quite a few times on different alts - mostly normal slow stable travel but had it once going swift from Thorins Hall to Michel Delving although in that case horse ran into stable building and kept trying to hit fence!! Worst instances were when (a) lvl 12 warden rode off rode into ravine just next to goblin camp; (b) lvl 21 captain en route to Candaith using one of Saradan's horses stalled close to where lvl 55 mobs hang out. Usually dismount and walk IF SAFE but seen suggestion above on relogging from character screen.
Will try that next time as had the problem for couple of weeks - did get booted once but on relog was travelling again.
I've reported it three times while IG - first time as a 'stuck' ticket when told no problem and other times as 'bug' but never been contacted by email or anything.
Wife has had same experience and in higher level areas (Lvl 35+)
I guess I've been lucky. I've had this happen, but I've always been within a very short distance of the destination. Then I feel like the humans in Wall-E for feeling annoyed that I have to dismount and walk those last few feet