The data on the US is a lot less clean than for Europe, so this is the best I could find:
https://www.epa.gov/climate-indicators/climate-change-indica...
"Between 1979 and 2018, the death rate as a direct result of exposure to heat (underlying cause of death) generally hovered between 0.5 and 2 deaths per million people, with spikes in certain years (see Figure 1). Overall, a total of more than 11,000 Americans have died from heat-related causes since 1979, according to death certificates."
(same site, different page) https://www.epa.gov/climate-indicators/climate-change-indica...
"Between 1979 and 2016, the death rate as a direct result of exposure to cold (underlying cause of death) generally ranged from 1 to 2.5 deaths per million people, with year-to-year fluctuations (see Figure 1). Overall, a total of more than 19,000 Americans have died from cold-related causes since 1979, according to death certificates."
A lot smaller difference than Europe, and there's the 1995 heatwave thing in Chicago which throws it all out of whack, but there's still more people dying from cold than heat, even in the USA.