Paths between veggie beds with clover?

I used to do woodchips in my paths between the beds, but they are very hard to come by unless I paid $100 for a truckload. Now if I would sow red clover instead in the pathways,  I would grow a good medicinal and bee plant too. But how high does it grow? Do I have to keep it mown (so I would have to measure the width of the lawn mower but most likely my paths are much narrower. I don't want it too high I find it cumbersome after rain and I don't want to step on snakes either.
BTW the woodchips are AWESOME if you get them. After a year you rake it on the bed and its the nicest soil.

You might want to consider Irish or Scottish Moss instead, very foot traffic tolerant and durable, low growing naturally and in spring they both put out very pretty little flowers.

Only Dutch White clover grows low, all the others will get up to above knee height without mowing.

Redhawk

Thanks, unfortunaletly the dutch white clover is not the medicinal one, but yes I find it in the garden and could transplant. Moss will probably not grow very well. I'll have to measure the lawn mower.... Actually won't be that bead I could harvest some organic matter!

What about using Creeping Thyme or Chamomile?