I have updated the Mt. Rainier NP photo guide with the January news, access and conditions, and monthly report Web pages. January is a continuation of mid-late December, and will continue through the winter until March or April. In short, it's winter and everything winter. The NP is in full winter operation mode with all snow activities available in all designated areas open, which includes snowshoers, skiers, snowboarders and the snowplay area.
Currently the road to Paradise is controlled at the gate east of Longmire. It opens daily, weather permitting, after the parking lot at Paradise and road between Longmire and the gate is checked and cleared of snow, usually between 9-10 am. It also closes every day to uphill traffic at 4:00 pm. In addition, the NPS requires all vehicles carry chains and may require the use for non-four wheel drive vehicles at the parking lot just west of the Nisqually Bridge to Paradise.
Through the winter the only facilities open every day are those at Longmire (hotel and visitors center) and the only facilities open on weekends is the Jackson Visitors at Paradise (10 am to 5 pm). Everything else is closed for the season. If you go you should be prepared for winter travel with a proper equipment in your car, with the right clothes for all visitors, and with the necessary emergency gear of clothes, food, water, blankets, etc. You should also be flexible with your plans and schedule in case the weather changes or the NPS folks instruct visitors.
There's lots of excellent photographic opportunities for winter and snow scenes. Just go and enjoy.