That damage needs more than paint. You must fill with the proper material, then paint. If you have experieence and a warm place to paint, go for it.
I have very sucessfully repaired bumpers with paint from Tower Paint. The nice thing about rattle can paint is that it is easily removed with lacquer thinner, but factory paint is not. If you don’t like your paint work, remove it and try again or involve a professional.
I live in South Florida where cold is not a problem, and I have done light painting for many years. However, you have a lot of damage. I would have a body shop fix it.