Winchester chambered the 44 WCF in the 94 Carbine for two or three years in the 70's. They also had a special run that they partnered with Colt to produce, a boxed set, 44 WCF SAA and the 94 in 44 WCF, I believe in 1976. Both were engraved with gold inlay. My personal experience is with the more workman like standard carbine.
Other than the abbreviated loading gate, and the shorter throw of the lever, the 44 looks and handles almost exactly like a standard carbine in 30 WCF. 10 44 rounds weigh more than 6 30's, so the gun is a tad heavier when full.
I don't know how many Winchester made, so I couldn't hazard to guess how many are still around, but it is true that they certainly are less than common.
