My hands get really cold, even when it's only 10C outside. For years I tried combinations of heated grips and different gloves. It didn't work well enough for longer rides. My hands would still freeze. I am sure muffs would help keep a lot of that cold air out. It's a relatively cheap and effective idea. Because most people don't commute here in winter, not very common, so I never tried them on the bikes that had heated grips.
Instead of installing heated grips, I have moved on to heated gloves. It's a lot more effective in heating your hands, they go with you from bike to bike (this is especially handy when you have multiple bikes and/or travel to ride other bikes) and work well even on early summer rides when you go places where it's still snowing and close to freezing outside. Not cheap, but considering that my first pair lasted 10 years and I am still using it, not unreasonable as far as MC gear goes. Plus, what price to retaining feeling in your fingers when you need to finesse that brake lever pull? https://www.warmnsafe.com/products/the-rider-classic-style-mens-heated-gloves
You get a heated jacket liner to go with it, and you are ready for anything winter can throw at you. Well, maybe not icy roads
, but other than that...