If you are concerned of any small infection on that small cut just put on a dab of ... toothpaste. A lot of people forget that teeth get dirty by bacteria in your mouth and toothpaste is designed to fight this. The small .99 cent trial size toothpaste that contains TRICLOSAN are perfect to carry in any daypack. If you will see that many liquid hand cleaners contain TRICLOSAN, although in higher concentations. I havn't used this in freezing weather yet.
My grandfather used Crest may years ago when he cut his leg doing work on his cabin/house. From then on he would drive grandmother crazy, and I mean ballistic, by running for the toothpaste everytime one of us kids scaped a knee. Boy did she give him earfulls of grief. Only after they both past on did both my dentist, and also my pharmacist, say it was a perfect O'l Injun trick. I really wish she had been around so I could give her the good news Grandaddy wasn't nuts after all.
Plus If you want to feel minty fresh breath for that big buck your hunting, just use your finger to brush teeth.