La Roche-Posay Lipikar Balm AP+ is your best bet.

For extreme cold itchiness on arms and torso, La Roche-Posay Lipikar Balm AP+ absorbs quickly and won’t leave you sticky. It’s rich enough to actually stop the itch without requiring a ten-minute rub-in.

The key difference here is that most “extreme cold” lotions (Eucerin, CeraVe in the tub) feel great at first but leave a tacky film that catches on your clothes. Lipikar Balm uses shea butter and niacinamide, so it sinks in fast and the moisturizing effect lasts through a second day. Fewer applications, less mess.

A runner-up is CeraVe Moisturizing Cream if you’re on a budget, but only in the tube—the tub version is too heavy for torso use unless you’re okay waiting an extra minute. Apply it damp, not dry, or you’ll still get that slight drag.

Don’t bother with anything labeled “lotion” in winter. You need a balm or cream with ceramides. This one does it without feeling like you’re wearing a layer of glue.