Y
Standing next to the door and saying "oh, I can feel cold air" doesn't quantify it enough to say whether it's a problem that will significantly affect the heating bill, and the insulation inside the door may represent a bigger improvement (lowering) of the heat loss of the property compared to the old door
It's possible to improve the draught sealing of the door yourself; for example I would say it's rare for manufacturers to keep a draught sealing strip continuous over a hinge - the strip is normally part of the profile, and gets interrupted by the hinge. Applying a slim foam strip that the hinge compresses when closed, to make the draught exclusion continuous, would perhaps reduce what you feel.. However, unless you live in an immaculately detailed passivhaus (which we know not to be the case, as such houses don't have heating bills) it would be overkill - somewhere else in your property there is a bigger hole/gap/crack that should be tended to first