I'm assuming there is antifreeze in the coolant? If so, and you have water in the oil you will have more problems than the headgasket (or whatever the leak is) to fix. If your going to fix it better go ahead and replace all the bearings when you have it apart. I've not had an issue like this on a quad, but in a vehicle if you get antifreeze in the oil you can about guarantee you will have bearing issues. I'm sure any four stroke motor will be the same. If it is just straight water and you get it cleaned out promptly it is not as bad as antifreeze, but still not good to have in your lubrication system.

I don't know how Yamaha is right now, but a lot of the ATVs and snowmobiles have gotten hard to get parts for in a timely fashion lately. Might check into that also if you need it soon. I know my 2016 Arctic Cat fourwheeler is down waiting on a new wiring harness that I order a month ago and is "supposed" to be in my the end of May.

Did it get cold enough to freeze it? One of my road race bikes froze overnight once, only allowed to run straight water. It popped a freeze plug out, was under the valve cover in head. If u had a cracked head or leaking head gasket I dont think it would leak so bad u cant fill the rad.