I have a TT not a MH, so stablizers "down" when in storage. I am able to store at home, but living in the country we get very high winds. I park the camper facing West-East as most of the winds come out of the West, hitting the camper head on.
My thoughts are, the more points of contact to the ground, the harder it will be for wind to move the camper (which did actually happen once at our previous residence when we lived in town, when I did not have jacks down because the camper was between two buildings, and I thought it was immune from wind... Boy was I wrong!).
So, the more points on the ground, in my opinion, the better. By the way, even though I now park the camper on asphalt, I still use blocks (wood) under the jacks. Tires sit on the asphalt.
It absolutely does not hurt anything to have all the jacks down. It doesn't hurt to have them up either. But like so many, we use our camper all winter at home, sleep in it almost every week end --- yea ... go through a lot of propane over the winter too heating it.... but it's worth it. So, keeping the camper stable, level, and operational is important to us.
By the way, I don't keep a stash of beer in the refrigerator in the camper. I really don't drink alcohol at all, except an occasional wine. BUT ... I do keep my stash of Coca Cola in there! Chilled all the time! It's my reserve supply! And for week-ends!