Check the windows for any cracks and air leaks, caulk the cracks and you can save on heating bills, whether you pay them or your tenant does. You can also take solace the fact that you’ll be helping the environment a little bit.
Check the weather stripping throughout the house to make sure it’s still in good condition, if not replace it. If you don’t have any, you may want to add some.
Have your air filters changed and cleaned. These are typically supposed to be changed more than once a year, so make sure you or your maintenance crew is on top of it.
If there is a draft coming from any of the outlets use expanding insulating form inside them or go the extra simple route with childproof covers.
By taking the lead and winterizing your apartment units you may encourage your tenants to do the same which increases efficiency, eases the burden on the environment and reduces bills for one or both parties. If there are winterizing steps that you cannot take as a landlord but would encourage your tenants to do you could send out regular newsletters letting them know what steps they can take. You can’t force your tenants to be as vigilant as you are but you can encourage.