I used to do re-creation/re-enactment stuff (when I could afford it and before it got political), wearing shirts with big, droopy sleeves. I also cant my bow when I shoot... All you need to do is either tie up the sleeve and keep it out of the way, or use one of those "full arm" guards that extend well above the elbow. Worked for me, both ways.
You could also wear layers -- cotton t-shirt and long-sleeve over-shirt with wool or wool/blend coat, instead of big, bulky things such as down coats. Clothing does not have to be loose or bulky to be warm.