Mulching after rain - compacting soil?

We've had continual showers for the last week and are forecast for the same for the next week.  There are a couple of beds that I had intended to mulch but haven't got around to.  I remember reading that you shouldn't walk on beds that are too damp, as it compacts the soil.  But you are meant to mulch when the soil is damp.  What should I do?  One of the beds is really big, so I'd have to tramp around on it a lot to mulch it.  The subsoil is clay but the top soil is not too heavy.

Many thanks

Use a plank if you can. This will spread your weight over a much wider area than the soles of your boots. 

The soil may be damp but it is also still cold, and mulching (unless you are using black plastic) at this point can stop it warming up properly, which your seedlings and young plants won't like but fungus etc will. I'd leave it until the weather is due to change, let the soil warm and then mulch