I found YouTube videos showing one way, but it appears to only work if your spouse is a merchant. In that case, you basically give them something better, they equip it, then you go into merchant mode and buy off their original equipment...leaving them only with the gear you've given them.
Of course, the problem is that not all marriage partners are merchants.
You can, naturally, get them to wear anything so long as it's better than their stock equipment, but when it comes to clothing, it has an armor rating of zero.
Is there a way around this? Can clothing be enchanted with a high enough armor rating to replace base equipped armor on a spouse?