I don't bother other than to scrape the mud off, Edged tools like scythes/bilhooks etc are kept in the house where it is dry or they would certainly rust over winter if left in the barn. but wooden handles get no care, If you were to look at my rakes and hoes you can see where they are wearing thin from use. they are going to wear to thin to use before they come to any harm from lack of care. I also cannot see the point of sharpening spades here, our soil is about 1/7 stone (I've been sieving it for an asparagus bed, every 6 wheelbarrows of soil I get 1 of stones) a couple of meters of digging and it's blunt again and chipped.
Since
gardening is my work I look at it this way, if I have to spend time caring for them then that has to cost less than a replacement tool/handle at 300dkk for a decent rake and 150dkk/h wage it just doesn't work out.