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Most years the higher trails in the Olympics and Cascades will start to be snowed in by mid-October. Sometimes this starts to happen in mid-September, and sometimes even by Labor Day. There are lower trails which remain snow-free much later in the year.

Most years, mid-October is rainy season, with day shortening fast and the potential for rain (and snow) which doesn't let up for weeks on end. You'll want to think about that, and always have a plan B in mind.You'll need to choose wisely based on conditions at the time, not predictions for what might be true two months from now.

"A little trekking" could involve short dayhikes, of which there are hundreds, or longer overnights. If the former, you'll meet other folks easily enough in hostels, at trailheads, or along the trails. If the latter, it's going to be tough. You might search out some of the hiking websites--The Seattle Mountaineers, Northwest Trails, etc.

Note that if you're really that inexperienced, the Olympics offer many, many opportunities to get in over your head and perhaps never come back. Be careful and stay humble.

Hope that's helpful.

Mark