As others have pointed out, heating requirements (watt/m^2) are in fact linear which is why it's possible to more or less accurately calculate a building's insulation performance in watt/m^2/K, it's just that there's a grace zone where if it's e.g. 65F outside and you want it to be 72F inside, you might not need to heat at all because the shortfall is covered by solar gains through your windows, internal gains (cooking etc.) and energy stored as thermal mass. That is, the nonlinearity is not in heating needs, but in the efficiency of heating production and the amount of heating you get for free.
Yes that is correct in theory, BTU requirements are linear based on delta temperature with everything else being static.
What doesn't follow is electricity consumption per BTU produced, ie. if your heating source efficiency is non-linear, such as a heat-pump + resistive fallback heating. You can easily consume 8x the amount of electricity with a delta T of 60 than you do at 15.
In reality, outdoor air temperature alone isn't indicative of the entire building heat loss/requirement - ground temperatures don't respond linearly to air temperatures. Likewise, there are some oddities that come into play with high temperature deltas such as phase-change of materials or outright failure in some cases. Precipitation and wind can also affect thermal efficiencies.
A bitter-sweet example for Texans: The snow can actually provide some insulation. It would be worse if you had no snow and similar air temperatures than getting that 12" of fluffy stuff later this week.
