You were using a dual suspension mtb.
Perhaps a rigid frame would work better.
Around here I rarely notice cross bikes in winter. They seem to mostly be MTB with or without studs when the weather gets bad.
I have a CF racing bike and an aluminum roadie fixie. I just do not see the need for a crossbike at the moment. A MTB seems a bit more versatile in winter.
Something like a Surly 1X1 frame with a lower gear and no shocks.