I'm not sure when they open the roads in the foothills back up. Maybe someone from WW can chime in there. As your subject says, to find somewhere to hike for an afternoon it would have to be on public land (i.e. National Forest). I'm not sure you can get there unless they've openned the primative roads.
Will you have access to a 4x4?
An option closer to town would be to hike around Bennington Lake or the Rooks park area. Its not really "forested", but you can find some isolated places to poke around and kill an afternoon. Good chance of seeing some deer.
Or, go into Oregon; you might be able to get to Tiger Canyon on Mill Creek. Also, maybe the South Fork of the Walla Walla river trail on the other side of Milton-Freewater. I just don't know how long they keep those roads closed.

Many of those roads will have snowpack issues at the higher elevations.
If you don't want to leave Kennewick and just want a good hike with stellar views, the Badger Mountain trails are awesome. You likely won't see much, if any, wildlife; but the hike is a lot of fun, a good workout, on well-maintained trails, and there are several trail options to the top.
Cheers!