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If it's actually a deep one you'll want some filler to fill the gouge and be able to sand it back smooth before priming and painting it again. As long as you don't have some extremely obtuse paint colour that's hard to match it should be relatively straight forward with patience and preparation although the biggest problem this time of year will be the temperatures unless you've a nice warm garage to do it in. Paint won't adhere at all well outdoors at this temperature.
A rather more prosaic post than the above: Can you fix a deep bumper scratch at home? Or at the very least conceal it a bit? Some kind soul has bestowed one on me. It’s like they’ve rubbed off a 3 inch line along the top of a ridged bit of bumper. Looks like you can see the plastic underneath.