How to Restore Old wooden handles on Farm Tools?

I would probably try cleaning the wood with a deck cleaner like Thompsons, and then treat them with a sealer (also Thompsons).

As an alternative, you could use some 100 grit sand paper to remve the dirt and grey wood and seal with poly urethane.

Finally, if you like the grey, don't do anything! If they stay dry (or at least are in an area where they will dry after it rains, they should be fine for many more years.

If you use chemicals, follow the package directions.

In my humble opinion, any restoration work on the wood would take away from it's unique quality of aging.

Farm implements have survived for a long time, because they were made to weather...and I think, look better when allowed to "show their age"...

If it were me (and I collect antiques), I would leave them alone.

Possibly a rake. Like a bigger version of the garden tool used for pulling weeds.

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you can sand them smooth, then take a wood cleaner/deck wash, and soak the handles in it. it will remove most of that greying. then restain them with an outdoor waterproofing stain

You can easily sand them. However there are lot of wood polish available in the market. Use them.