storing desk outside  

Desks
of that type almost always come apart.
Surely it's be preferable to knock it down and store it inside?
(If you're eBaying it it'll only be in the way for a week or two anyway)

Avoid it if at all possible.
It's just asking for trouble.

Just throw it outside on the...
Just throw it outside on the lawn-sit down and put your feet up. Looks nice, no?

I think it will be fine. Jus...
I think it will be fine. Just be sure that whatever you put around it is completely sealed, and that you have some kind of heater inside that will keep it at a reasonable indoor temperature with reasonable humidity. And that it's not right next to the heater. And keep it off the cold ground. And of course keep the enclosure tented on top so that rain and snow will not accumulate.

and
that any passing rodents don't fancy a nibble...

I have this outbuilding that...
I have this outbuilding that I put a couple of old dressers in for storing tools and misc. The structure has vents under the overhanging roof eaves that allow a free flow of air through the building (is it just bare stud walls and joists inside). The moisture in the air was enough to cause veneer to start curling and peeling off of the dressers after one Winter.
The building is technically 100% watertight, and even has a plastic membrane embedded in the concrete floor slab to keep moisture from rising up through the concrete, but I would not think of storing a valuable piece of furniture in there year-round.

Having seen the
Damage that can be caused by damp and cold from joints expanding and chipboard sucking up moisture I think you should leave the desk to someone who can use it and love it.
I was offered some rosewood furniture that had been stored in un-heated warehouse and all the drawers were locked and the joints on corners had blown apart from the wood expanding. The rosewood was ripped over the grain and thus rendered the whole piece firewood.
So forget about storing it and let go to someone who won't destroy it

Nope
Why risk it? Seriously...If it's a nice piece and you're selling it for a reasonable price, then just deal with it being in the way for a bit. I would think that you shouldn't have to wait too long.