I use a cross bike as my winter bike, with 32c road tires and fenders. I've got thousands of miles on that bike, and thousands more on a much nicer cross bike too, but I would never do any kind of road race on either one, not even on a gravelly type course. If speed matters I'd take my daily rider road bike with 28s over the cross bike for literally anything short of actual cross racing or single track. On the cross bike I can keep up on a fast group road ride but it is absolutely a handicap. The extra weight, more upright setup and less aeroness in general just all adds up.