I don't know what sort of heat pump systems are common in the US, but Sweden (and AFAIK Norway and Finland as well), are probably >%80 heat pump for single family homes (most apartments are community heating at least in the larger cities). So it's absolutely now problem to run a heat pump even if it is very cold outside, but if you want to improve efficiency in areas that are super cold you can drill into the ground for a heat sink (those are called Bergvärme in Sweden).
Regarding cost, in most of the countries I've lived in a large fraction of the cost in the gas bill was the distribution cost. So once you switch to a heat pump, you also switch to electric cooking and even if heating with electricity would be significantly more expensive you would still win. Is that different in the US?
It varies significantly by locale. I've seen people post online about how it made little sense to keep just one gas appliance because of significant savings. I'm in Iowa, which typically heats on natural gas in urban areas. I have a natural gas central furnace and water heater. My clothes dryer is electric, and I have a 3 head heat pump which I use for comfort in a couple rooms. The house is an early 2000's standard builder-grade home.
For September, $12.31 of my $27.01 gas bill was variable based on my consumption.
In December, $84.82 out of my $99.65 total was consumption driven.
I've run numbers on whether it'd make financial sense to go electric for heating, and the break even point is in the 30-40 degree vicinity. With temperatures 20 and under a healthy chunk of the year, unfortunately the added expense doesn't make financial sense.
Regarding cost, in most of the countries I've lived in a large fraction of the cost in the gas bill was the distribution cost. So once you switch to a heat pump, you also switch to electric cooking and even if heating with electricity would be significantly more expensive you would still win. Is that different in the US?