Insulation does not stop drafts! Fiberglass insulation in particular acts like an air filter - the drafts move right through it.
A physical barrier must be installed to stop drafts but the interesting thing is the barrier does not necessarily need to be where you feel the draft.
Your home experiences what's called The Stack Effect. It's a natural phenomenon that causes air to leak into the bottom of a structure and out through the top. To stop drafts use the ABC method.
A is for attic. Since this is where the conditioned air (and your energy dollars) are leaving your home, it must be sealed first. This is done with spray foam on top of every wall in the attic as well as around wiring and plumbing penetrations. Recessed lights, pull down stairs and attic hatches all must be properly sealed to keep the air inside the house.
Sealing the attic results in less air entering the bottom of the house. Since it can't get out, less leaks in! Your basement and first floor will be more comfortable because you sealed the attic.
B is for basement (or crawlspace). Spray foam around the perimeter of the wooden joists prevents air from leaking in. Crawlspaces should be sealed and encapsulated so they are warm and dry. New basement windows are also often part of a prescription for defeating drafts.
C is for conditioned space. This includes windows, doors, outlets, etc. Notice these items are all last. You can feel these leaks because they're in the living space. But they are tiny leaks compared to the monsters lurking in your attic and basement.
Never insulate without sealing your attic. The insulation will make your attic very cold in the winter. But since it doesn't stop air from moving, any moisture in the air from cooking, bathing, laundry, etc. will find its way into the cold attic where it condenses on cold wooden surfaces and starts mold growth.