My point was that you do not have to ruin anything. Just remove one chainring (buy some some shorter BMX chainring bolts), get a new fixed wheelset and remove the clipons and screwons and you are ready to
go. This looks to be a frame from the late seventies so it might even have room for studded tires. (My 73 Crescent 531 frame has). Riding a fixie in winter is fun !