The last time I was anywhere near Cooma in winter was in a Butler Airlines Vickers Viscount some 50 years ago. But enough of me and my reminiscing;
Ring Mike Apps, Polo Flat 02 6452 6636 or 0412 435 198 for permission to land about 1km from town, or go to YCOM a lot further away, big taxi fare, or better still just buy an AOPA Airfield Directory.
Edit to add, Jindabyne is closer to snow, but accommodation probably more expensive than Cooma. car hire could weigh heavily on your decision. Oh, and fly the single in winter unless you're better than just current.