Rolling resistance - Wikipedia
Excerpts:
Sidewall deflection is not a direct measurement of rolling friction. A high quality tire with a high quality (and supple) casing will allow for more flex per energy loss than a cheap tire with a stiff sidewall.[
citation needed] Again, on a bicycle, a quality tire with a supple casing will still roll easier than a cheap tire with a stiff casing. Similarly, as noted by Goodyear truck tires, a tire with a "fuel saving" casing will benefit the fuel economy through many tread lives (i.e. retreading), while a tire with a "fuel saving" tread design will only benefit until the tread wears down.
Temperature: with both solid and pneumatic tires, rolling resistance has been found to decrease as temperature increases (within a range of temperatures: i.e. there is an upper limit to this effect)
[50][51] For a rise in temperature from 30 °C to 70 °C the rolling resistance decreased by 20-25%
The introduction at the top of that wiki page is probably worth reading too. It goes into the impact of Silica vs Carbon Black and so forth.
If you just make the tread compound softer/more adhesive then yes your rolling resistance will go up.
If you keep the tread the same and use a more compliant sidewall, then you will reduce rolling resistance as the energy required by the sidewall deflecting to create the contact patch goes down.
In summary if you soften the tire in the right ways it becomes easier to roll, as it takes less energy to deform to create the contact patch. Running winter specific tires allows you take advantage of low temperature compounds that deform more easily under their intended conditions and as such use less energy than a tire operating at the very low end/below it's temperature range.
