I flew out of Chicago with 2 cats. BA and BMI both have heated transport vans, so as of 18 months ago, you could fly pets in winter with no restrictions. I, personally, wouldn't survive the worry and stress of a connecting flight with cats(I barely survived a direct one, and I was on it with them!) Plus, I'd worry about the stress on them being loaded twice and moved around.
I will say, BMI was great, and the pet transport people in Chicago were soo caring and helpful..