Had a great early ride Bristol way on my cx too this morning, cant fault the bike for these conditions – would have been lethal on road bike and cant cover as much ground on a mtb.
After recently putting together my first cx bike, a Kona Jake so nothing flash but with some nice parts I think a cx bike would be perfect for what you describe. Similar to your requirements I wanted something robust for use as a winter / training bike with 700×35 tyres that handle winter better than 23’s, less punctures etc. I also find myself riding more interesting loops that contain bridleways that a full on road bike would not cope with and if you set it up right could also be an all day comfortable tourer.
And when spring comes and the carbon comes out I will lose 8lbs instantly!