[Shandy]

I have an acer which is about 4 foot tall but it appears that half of it has died.

Can I cut off the dead wood now or do I need to wait until the tree is dormant?

If I cut it could it kill off the rest of the tree?

Hard to know what is best.

[sunshineband]

Check that the wood is really dead before getting out the cutters: scrape the bark with your nail, and if it is green underneath still, and not dry, then leave it to see how things go

The lighter coloured twigs look dead from the picture, but the branches with red bark look quite healthy

[Aunt Sally]

Oh dear 

When pieces of my acers die back I prune them off and they re-shoot quite quickly.

[fatcat1955]

Cold wind can cause this. I see you have a fence behind the plant but this can sometimes trap the wind. If it has been done by the wind you will need to erect a temp wind break in front of it till all danger has passed.

[starry]

definitely check to see if it is  dead, I always go around snipping off the dead bits on my acer but some times as I go to snip off some very grey, dry looking bits, a closer look usually reveals some tiny buds    but you can trim it this time of year and they do grow back.