If I was buying a bike specifically as a winter bike, then yes 28mm is a nice to have, but I’d also want full length propper mudguards, which no race bike will take as you need taller brake callipers to clear them.
It isn’t the be all and end all, and TBH most of the roads aren’t any better in the summer. The difference between my bike in the winter and summer is a set of SKS raceblade longs which are an OK compromise and fit over narrower 25mm tires (i.e. that actually measure 25mm). Summer tyres were either 23 (that came up big) or just lighter 25mm tyres. The recently fitted ‘big’ Schwalbe one 25c weren’t intentional, I was happy with the true-ish to size hutchinsons.
If you’re on a budget, look for anything with long drop rim brakes (easy to spot, they wont’t be 105/ultegra, they’ll be labeled R-550 or similar) , they should allow proper full length mudguards to fit under the caliper and still get 28mm of clearance. Disk brakes obviously solve this problem in a much neater way, but a disk braked bike with 28mm+ clearance is going to be quite a bit more £££, although you might get lucky if you can think of/find something unfashionable on ebay (Eastway frames often go cheap despite getting good reviews for example).
If you just want “a road bike” for clubruns etc I’d get the planet X, it’s a good enough road bike, and should fit (actual) 25mm tyres and raceblade-longs as a good-enough compromise. Obviously “real” roadies will have n+1 road bikes for every eventuality. And obviously MTBers like to pretend they’re not real roadies by trying to differentiate themselves with poorly thought out, or over thinking component choices. It’s “reliability trial” time of year, which magically means everyone’s summer bike and 23mm tyres comes out and the mudguards are off for one weekend of the winter and somehow no one dies.