Looks like you are on the prairie like me. Use what you have in abundance, you can mulch with sod chunks. Also if you pull sod from the paths between the beds you will raise your beds that much higher by just transferring the sod chunks to the bed. flip them over and move them around as needed they have an excellent mulching effect. If the grass starts to grow back just move it around, flip it over, cover with more sod. Maybe you don't have to leave your place to get material. You have all you need right there for free. Use what you have in abundance. Take what there is lots of.
If you do have a tractor and can mow, you can just mow and rake it up into a wheel barrow or cart and take it to your garden bed.
Looks like you have animals there. If you remove all their old bedding, and put it on your garden bed, that will feed your garden now so you can plant in spring. Bed them fresh and when it gets dirty add it to the garden bed. That way all the mulch/straw/hay you do have to buy or transport you can be using it twice. first they sleep on it and inoculate it with poop and then it feeds your garden. Also used stall bedding stays in place a lot better in the wind