My twin daughters are almost 2 and we've had our share of colds this winter. I can't always get to them to wipe their noses before they wipe it on their sleeves… yuck! In the past, I would just change their shirts but then I had an idea – I put their old leg warmers (these I made when they were younger – I bought girls' knee-high socks and cut the feet off of them) over the sleeves of their arms and viola! Worked like a charm!
If you're looking for a little more style, I see lots of kids wearing "arm warmers" these days. BabyLegs fit the bill perfectly. Tons of patterns, great quality, lovely mom-invented business.
More: Cold and flu hacks