Glad to help you find a camping site in Southern Oregon! Currently, it’s pretty wet and chilly in the Medford/Ashland area, but fun camping spots do exist. Just expect full rivers and streams and some rain.
For seclusion, I love camping at Squaw Lakes, just above Applegate Lake outside Ruch, Oregon. It can be found just past Jacksonville. There are a collection of walk-in sites, all spaced around the small lake. Fire pits and picnic tables are in place, and there’s a water faucet and pit toilet. Otherwise, no structures exist. In summer, this area gets crowded, but in winter and spring, it’s empty and there’s no fee for the sites. Since the elevation is pretty low, there’s very rarely snow.
Later in the spring, the campground at Mt. Ashland offers the same level of seclusion, but it’s not usually accessible for camping (other than snow camping) until April or May. This year, it may even be later!
If you need something close to I-5 just to lay your head at night, try Valley of the Rogue state park. There are even yurts to reserve.