My preference is to leave quarters bone in. If they are too big to fit in the cooler, you can cut it at the knee joint and remove some bone. I prefer to do it this way becuse it minimises surface area when compared to boning out meat. The surface area seems to collect dirt, hair, and debris so the less surface area the more meat i will be able to put in the freezer. Triming the outer layer off a whole quarter vs 10 hunks of meat is much more efficient, less time consuming, and results in more meat in the freezer.
There will be some blood but as long as there isnt standing water the meat will be fine. I prefer whole quarters in game bags ontop of ice. I will leave the drain open while I'm at camp and close it once I'm headed for home.
Everybody has their own way of doing it, so my advise is to do what makes sense to you and your style