Yep, it's not ideal in the cold weather, but presumably split-system fridge itself is well insulated and thus not cooling the house interior significantly. And house heating system is capable of delivering heat to the right places more efficiently than in the case of traditional fridge "we heat the kitchen because that's where the back wall of the fridge is." But of course only real modeling and prototyping will tell for sure.
Agreed, heating is much more efficient than cooling anyway, so you'd still get a profit with your system, even though your heating exoenses might rise just a bit.
