Schwalbe Marathon Winters are designed so that if you pump them up hard the studs have less contact than with lessor pressure. It's not as smooth as no studs but isn't at all bad. If I think conditions are likely fairly dry but I'm not sure then I'll pump mine up and enjoy a nice ride. If there's lots of ice or slush I can let a bit of air out for better stud contact.

I've been going with just a front stud on my Opafiets (got lazy one year about changing the rear) and this has worked quite well and this is in Minnesnowta. For OP this could be a less expensive option than buying two wheels and a front wheel can be had fairly inexpensively.

For me, when there're any ice patches, I'd not want to go without studs at least on the front.