Per the Equinox manual (p. 65) the minimum operating temperature is 14F. Note also, that charging the battery is NOT recommended below 32F, so if you rigged up your detector with an external power pack on the stem to enable charging the detector while on-the-go, do not connect the battery pack to the Equinox if the air temp is less than 32 otherwise the chemical reaction in the battery during charging will go awry and you will permanently/prematurely lose battery capacity.
In contrast the Garrett AT Max manual says to avoid using the detector in sub freezing temps, but I have seen plenty of folks using it in the snow and obvious sub freezing situations and it seems to do just fine. It also uses alkanes or NiMH AA rechargeables which have a lower capacity in cold conditions but do not suffer from the issue regarding cold temp charging from both a chemical standpoint and because Garrett doesn't support on-the-go charging.