If you aren't staying in the area then get in touch with the local letting agents and let them handle it as they will then look after advertising, contracts and any eviction or putting to rights that needs done at the end of each season or let. You will not begrudge the money if you get a smooth process and one person to do all the work for you.
Letting seasonally ensures different bids each year and the market rate in income, aswell as ensuring the land isn't damaged over winter by either livestock or things like 4x4/tractor access in bad weather/mud. There would probably be greater demand for continuous use as it's sometimes hard to get somewhere just for winter and a hassle to move stock on and off, but you also get people starting to feel a sense of belonging which is nice until unfortnately sometimes it turns to a sense of entitlement and you want to sell or relet or return to your own land
You can also let parts separately - the woodland to pigs and the rough grazing to sheep, which may net more income than letting it as a whole and someone only having use for either or..
If you were near me and I was advising, I'd want the lot and on a 364 day basis with informal permission to stay over the one day but respecting that meant no long term tenancy rights. I did actually have such an arrangement for 9 years and could have fought for the right to stay on but I have never worked that way and despite a mere 5-6 weeks notice I did shift everything, on New Year's Eve, in deep snow on a rough single track hill and with a friend driving a livestock lorry who couldn't help as he'd not long got out of hospital after a hip replacement - long enough to drive but not to load and handle young ponies! One of the hardest and saddest days of my life but I'm afraid not everyone would go to the trouble of seeing you right so make it clean and in writing with an agent who can and will arrange, enforce if necessary, and probably know all the likely applicants and who to take on or not as a bonus feature of the service