My experience with shoes for my 4 pound yorkie with tiny little feet.
I have these sandals in size 1 and they stay on well.
Mesh Doggy Sandals
And we have the rubber balloon type things too (I have temporarily lost the name) in tiny and they stay on pretty well. She managed to get one of them off but it was after a long time.
Unfortunately the smaller the pup the "fancier" things you have to by. The "generic" brands just don't come small enough.
It's not cold enough here in Houston to need to invest in boots, but if we did these are personally my favorite because they are much cuter than any others I have seen.
Ribbon Bow Hiker Dog Boots plus it looks like it comes in a 0 which would probably me best if she is 3 pounds since the size 1 sandals I have for my 4 lbs Somi are just barely small enough.
Hope this helps!!