Can you get your garden paved in winter?

I’m considering getting my small, tatty front garden paved over /concrete poured and replacing the old iron fence which lets all the rubbish in. Is this something that can be done in winter with all the rain and cold? Would it be more expensive at this time of year due to weather protecting measures etc?

I will be keeping/adding as much greenery as possible, I’ve just dug up and replaced the grass so many times, but the community weeds just take over, and the side bushes are just badly planted and some are diseased. I just need a fresh start. I want to smile when I look at my garden.

ETA: I’m open to alternative suggestions that would enable me to keep the grass.