How cold is "cold" outside. Thermostats are cheap, I've seen them go bad after a single season, stick open and the motor never warm up properly.
If its -20°F (I really don't know the actual figure, but really really cold) even the thermostat being totally closed the motor might NOT warm up completely. This is where you see people putting covers, blockers over their radiator to help the motor warm-up. If no other drivers in your area are putting blockers, covers on their radiator, then I would suspect that something is wrong with the cooling system, most likely the thermostat.
Change of seasons is when you notice a bad thermostat, it gets in a rutt, opening and closing a certain distance again and again that it sees in summer, then when winter comes and it has to close farther than it has the last 1000 times, it fails.
Remember the thermostat only blocks the outlet to the radiator, NOT the inlet, that remains open always. Of course blocking just the outlet will pretty much cut off the flow to the radiator; BUT in extreme cold, enough of the cold coolant in the radiator will get sucked into the motor and mix enough to keep the engine cooler than the thermostat is set at.
I cracked exhaust manifold, if you have EFI and an O2 sensor, and the crack is upstream or near the O2 sensor, will cause the motor to run very rich (the O2 sensor senses the oxygen leaking in with the air leaking into the crack exhaust, extra oxygen means your running lean and that tricks the ECU into thinking it has to add more fuel to get back to normal). Running rich can make less heat than running normal or lean, BUT, your cooling system should be able to easily adjust, unless you're in EXTREME cold.