These steps will help keep the garage temps from the house:
If the house side of the utility room door actually gets cold, then it's not insulated. Replace it with an insulated door normally used for exterior purposes.
If the house side is reasonably warm, then repair/add weather stripping around the door itself, including the sweep under the door.
Eventually, you may want to insulate the garage itself (if it's not already) and add some insulation to the roll up door, too.
If you don't have any, some "garage door weatherstripping" will help reduce the air flow from outside to inside. This gets installed on the outside, attached to the "jamb" around the door and has a rubber flap that seals pushes against the door itself. Not a lot of insulation value, but it keeps the breeze and rain from blowing through. I just had to replace ours (after 25 years) earlier this summer since the rubber seal was perished.
You can probably install insulation (I've seen both fiberglass batts and foam boards) into the cavities in the door itself. This may require adjusting the garage door opener or lift springs (if you have a torsion spring) since it will change the weight of the door. It shouldn't be a significant weight change, but remember, whatever weight you carried into the garage is now going to be attached to the door itself.