To you gain lesser cover against enemies on foot while mounted?
When you’re mounted, attackers can target either you or your mount. Anything that affects multiple creatures (such as an area) affects both of you as long as you’re both in the area. You are in an attacker’s reach or range if any square of your mount is within reach or range. Because your mount is larger than you and you share its space, you have lesser cover against attacks targeting you when you’re mounted if the mount would be in the way.
Because you can’t move your body as freely while you’re riding a mount, you take a –2 circumstance penalty to Reflex saves while mounted. Additionally, the only move action you can use is the Mount action to dismount.
I think the answer there would be "sometimes, depending on the enemies and what angle they would be attacking from."
Ah yes... The worst possible answer ;)
That is how I'm currently planning to run it: lesser cover against adjacent medium sized attackers.