Freezing is a fantastic option and allows you to play the game without penalty for going on vacation, having a busy day, getting bored, etc.

Everyone is able to freeze their account for free, as long as they want, and as often as they want. It can be accessed via Account > Settings. Alternatively, individual horse tabs can be frozen, if you wish to only keep a certain amount of horses from aging/needing care while keeping others still active. That can be accessed via Estate > Manage > Tabs > Pencil Icon to Edit Tab under Actions.

Horses cannot be used as studs/broods while frozen, and I don't believe they can be sold (but not positive on this).

great! thank you! I didn't know that you could freeze horses in tabs, or how to do that.

not being able to sell frozen horses isn't a major factor in my setting up a sales account, it would be more like a an added bonus to conserving space for when I get into projects (and when I inevitably collect horses like the trinket goblin I am). Thank you again for the info!

I'm pretty sure I have bought a horse that was frozen before. Could anyone confirm if you can sell/purchases frozen horses? 

You may be able to physically buy a frozen horse, but they won't show up if you search for horses for sale, I believe. I couldn't find anything on the wiki to confirm or deny, however.

I've had people buy my horses while my account's been frozen! They shouldn't show up on the stud/brood or sales lists, or to search, though, from what I remember.