November is not that bad for Iceland. You will be able to withstand the temperature during the day and most of the night, but the downside is visibility. For November, you can expect it to be pitch black by about 6:45 PM and stay that way until about 6:30 - 7:00 AM. Consider using reflective clothing if you plan to hitchhike in those hours.
Traffic will not be as heavy as it is in the summer months and you can expect lengthy waiting periods between rides. I recommend waiting for a ride on the edge of the town/village and not riding with someone who can take you to an intermediate point. I.e., try to be hitching in a settled area.
You didn't mention which national parks you wanted to visit. Lots of them are inland and it can be horrendously difficult to catch a ride in and out of them for that reason. And while some of the visitor centres are open all year, you may be stuck there for a long time after about August. People like to drive around the edge of the island, from one town/village to the next. If you are headed inland, consider public transport or arranged. Also note that the weather at inland locales is a lot different than around the edge, expect snowfall and the reduced conditions it brings to hitchhikers. Finally, I used a motorcycle for exploring inland Iceland (I brought it with me, not rented), it's a wonderful alternative to hitchhiking and something to consider if your agenda will take you to remote locales.