I'll preface this by saying I've never used mounted in Palaeo Diet so this is off the top of my head!
There is nothing in the three standard sets so my thought would be to go back to the Songs of rules set for ideas...
These give you 'Long Move' - use the long measurement (lope) as max move and 'Mounted' - free disengage, bonus in combat and the ability to carry another figure.
I think I would use lope x 2 as max move, possibly not skulk (no short move) and a +2 in combat (base contact only as per club armed). If they loose combat the rider is dismounted and the horse possibly runs away (not sure - needs playing). Bulk of at least 2 possibly 3.
I would also look to add reactions on both sides - the horse would be a 'beast' for fire / hounds howl - moving away from the threat at max speed and force a reaction from beasts at 1 x long range no matter their rate of move due to size.
Depending on how trained they are you could look to add the 'excited' trait or the 'timid' trait to mounted characters.
Carrying things is an advantage - either another figure could be carried quickly (though would dismount to fight) or carrying extra bulk without slowing. I cannot remember any rules for 'collecting' things slowing you down though.