I've been trekking in Nepal both solo as well as in a group. Solo trekking in Nepal is indeed doable, but here at trekbooking we always recommend to trek with others, as it does indeed increase safety. Over the last few years there have been a couple of unfortunate incidents in the Langtang region where solo trekkers have been mugged.
I can see that you have made a trekking partner request and I am very confident that it will allow you to find partners for your trekking adventure in Nepal. For more about solo trekking, the article available via the following link, may be useful: http://trekbooking.com/blog/trekking-partners-solo-trekking-nepal/
Despite the unfortunate incidents in Langtang, Langtang is in fact a great trekking route, with 10 days available, and generally, the safety is fine.!. An alternative to Langtang is Annapurna Base Camp. There is, however, a risk that the base camp at Annapurna is not reachable in December due to too much snow (that may though contribute to making it an adventure as well:)). In that regard, Langtang is more accessible, and the trek also offers an option to climb a 5,000 m peak.
A second alternative could be to do the Gokyo circuit trek, via Lukla - Namche - Renjo la pass - Gokyo - and back down to Namche. However, the Renjo La Pass could be blocked by snow during winter as well.
All in all, considering that I am sure that you will find a trekking partner, I'd personally recommend doing Langtang, as it is a great trek and always accessible during winter.
I hope the above was helpful. If any further questions, please let me know.
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