There are however muffs (Tucano Urbano) that have cups built in, to clip onto the bar ends to stop wind blast pushing the muff back onto the levers
I've used cloth handlebar muffs for about 20 years with no such cup mods or wind blast problems encountered.
I simply strap them on and have used the same muffs on several different bikes over the years.
Once you get familiar with using them, you won't even notice them... except for the warmth

Plus, you can ride year round with the same comfortable pair of thin summer gloves.
Tom
Heated grips and handlebar muffs .... Don't go skiing without them

. These are my lighter weight pair .
Handlebar muffs also provide excellent rain protection. These are my heavier weight pair.