While mounted on a horse, do you really miss events & encounters?

I read that if you're riding your horse around, random events/encounters either do not happen or certain types never happen (or events happen less).

Is this true? Or is it the exact same as walking around?

Source: http://www.reddit.com/r/skyrim/comments/mirsj/i_have_but_1_complaint_after_40_hours_of_playing/c318vv5

You are immune to the random encounters on the roads like thugs/bandits stopping you

Solution 1:

I don't use my horse all that often but when I have I've had random events happen. IE and assassin tries to kill me or I find a group of thieves waiting to ambush me.