Stump warmers - for my arm I can mail order baby leg warmers [product info]
While knitting one's own tube socks can be an affordable and convenient thing, ordering them online is a real option as it turns out more people like to sew and knit stuff than meets the eye. So, why not take advantage of that.
Search the Etsy.Com website for 'baby leg warmers'. I found they fit my stump extremely well. There are some really elegant designs there. Mostly prices are very reasonable.
The best thing about them is that they keep the arm warm while I can still use the stump end for typing (without freezing too much) or kitchen work (without messing up the sock too much).
The SockDreams website has some great leg and also arm warmers. Check them out for styles, sizes and prices.