The HVAC blower motor is very easy to replace on the Equinox. Remove the glove box, then remove the motor from underneath. You may want to remove it and see if it is seized or doesn't turn freely. The blower cage is not serviced separately, but is sold attached (and balanced) to the motor. If you get one - get an AC Delco unit - don't buy a cheap, aftermarket unit.
How old is your passenger compartment air filter? With the glove box off - you should check it and change it if it is dirty. Instructions are contained in the vehicle owner's manual - but it is very easy to change the filter.
I have NOT worked on a Equinox heat but I know OTHER GM's have gone to computer controlled motors and do NOT use a resistor pack anymore
and if there IS a resistor you still would get HIGH speed operation as that bypasses the resistor
if it is computer controlled then usually you will have 4 or 5 wires into the motor 2 will be power and the others will be smaller gauge and be signal
the power is powered when ever the car is powered up