FWIW, my Cupra Tdi is exactly the same as the OP describes for about the first minute after starting. I just give it a few extra revs when pulling away for the first couple of times and after that it's fine. Mine was fine all summer, so it's definitely a cold weather thing. If you try and drive it as if it's warm, it will stall when pulling away, which is fun at junctions...
My 2p.