Yes, the underfloor heating is probably the best suggestion. I'd say go for the electric type though, as although the water type systems can be slightly cheaper to run, they can be a pain if they go wrong or worst leak.
I think electric is the probably the way to go but make sure the product you get has an earthed screen as a safety measure. It should have protection against both water (i.e. water proof) and against damage (i.e. something to shut off the circuit.
With regards to heating the rug up, I couldn't imagine how to do it short of an electric blanket (i.e. NOT recommended). But that would be too much of a risk IMO and the cost of the eletric underfloor heating is not prohibitive at all, will add value to your house, is safer, and has a host of features such as thermostat control, timer, etc etc.
Regards
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