Most packs would have considerable reserve in power output over what the motor/heater is capable of consuming - the maximum power drawn from the battery is already electronically limited to significantly lower than what the battery could deliver to give it this headroom.
One reason for this is that internal resistance of the cells does go up dramatically when they're cold. For example cell resistance roughly doubles at a cell temperature of 0C compared to 25C. Yet despite this EV's don't seem to limit the discharge rate significantly until you perhaps get to even lower temperatures.
By the way, the original premise of internal resistance increasing as the battery degrades is not generally true with Lithium Ion cells used in EV's as they are specifically optimised to avoid increases in internal resistance. If it's just "normal" degradation there is usually no significant change even if the SoH is as low as 70%. However a cell with a defect or which has suffered an "event" that has damaged it can have higher than normal internal resistance.
For example in my Ion pack there is one single cell which seems to have significantly higher internal resistance than all the others. This is evident when rapid charging (at an initial rate of 43kW) as the voltage on that one cell immediately pokes up above all the others and hits the maximum 4.1v cell limit quite early during the charge while the others are still at 4.075 or so. This also has the effect of causing premature throttling of the charge rate when rapid charging as the BMS strives to avoid that individual cell going over voltage at the expense of slowing the overall charge rate even though the other 87 cells could handle a faster rate to a higher SoC.
If there is any change in cell resistance of a cell that has fallen to say 70% SoH, then the increase is much smaller than the increase you'd see of a good cell being subject to low temperatures, which does dramatically increases the resistance, and this higher resistance is allowed for in the design or the car.
