This would depend on the era. In WW2 it was common to have all the tools painted the same color as the vehicle. Many times the equipment was left on the tank as it was overpainted.
Today, it is not uncommon to have some tools in overall forest green as well as some tools that look like they came off of the shelves of your local hardware store. These tend to be wooden handled, with black or laquer coated steel shovels, axes and the like. Sometimes the crew will paint these all OD green or flat black using cans of spray paint like you would find in Wal-Mart. There can be quite a variety since a broken ax or shovel can be replaced by one from virtually any civilian hardware store that accepts Visa.
I"d say it all depends on how much of a stickler for accuracy you are. Me, personally, I could care less as long as it looks like wood. I use Citadel (Warhammer) paints for tools. A basecoat of Bestial Brown, basically a dark brown, with some very very faint and light streaks of the base coat lightened with some yellow. But as Rob pointed out, it is not at all uncommon to see tools painted the colour of the vehicle, so as I said earlier, it’s all up to how accurate or aesthetically pleasing you wish to get.
I’m gonna’ go a little different route. I read this somewhere, have tried it, and like it. Paint the wood parts flesh color, then when dry, streak some darker brown over the handles, etc with the wood grain. Kind of backwards from what you’d think, but it seems to look okay. Something else to try, anyway!
I go even further out of line. I paint the wooden handles bright yellow and then streak on a rather thick wash of burnt sienna. Playing with the wash with a paint brush as it dries, you can create very nice looking wood grain. I paint the metal parts black first, dry-brush with steel and then highlight the edges with a dry-brushing of silver. Look at the shovel on my Sturmtiger diorama in the Diorama Forum for an example, though the grain effect is not very visible. Even though I agree as Rob stated that tools are commonly overpainted while on the rigs, I like to make them stand out.
I paint my wood handles differnt shades of grey. The handles on shovels and such will turn grey when left out in the weather. Unless your going for the new look.[:D]