When to mount your horse?

This can be very situational. However, there are several pros and cons that can help you decide.

Pros:

• Carrying capacity is set to maximum when riding. If you need to haul a lot of loot, this may be helpful.
• Your magic resistance applies to your pet while riding. This can useful when you expect magical traps, like poly and teleport traps in the lower levels of Gnomish mines. If you do teleport, your ridden pet will come with.
• A flying pet allows you to fly while riding.

Cons:

• If you are not a Knight, mounting the pet makes it less tame. This could be risky if it's been alone on another level for a while. It may lose its tameness.
• You cannot BUC test items with a pet while riding it.
• Most effects don't transfer from you to your steed. Your boots of water walking won't work while mounted, and levitation becomes...complicated.
• The pet will not attack first or pick up items while ridden. This can be good or bad, depending on the situation (stealing from shop, in desperate need of a corpse to eat, etc.)
• While riding, you move at the pet's speed. This can be awesome (warhorse) or not so much (dragon).