Can low temperatures induce a withdrawal reflex?
The withdrawal reflex is a nociceptive flexor reflex and is a spinal reflex intended to protect the body from damaging stimuli.

In other words, activation of heat receptors is not the trigger of the withdrawal reflex, it is the activation of pain receptors at high, tissue-damaging temperatures.

Extreme cold is also damaging and causes skin lesions akin to heat-induced burn wounds. Again, at a certain tipping point extremeley low temperatures become damaging, and cause frost bites (Sachs et al., 2015). At this point tissue damage will activate pain receptors and these cause the withdrawal reflex to be initiated.

Reference
- Sachs et al., Dtsch Arztebl Intv; 112(44): 741–7