A we walked the Annapurna round a couple of years ago around early Sept. Very little snow on the pass. However, the trail is steep and very slippery. No way I would take a bike up there if it is even legal. There are a few stretches in the lower elevation where it should be ok.

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Couple of comments:

The height of trekking season is October/November in fall and April/May in spring. You mentioned February, the high mountain passes are typically locked in late winter snowpack awaiting the spring melt.

I can't speak for Annapurna specifically, but the high altitude trekking trails are technically possible to "ride". Some riding has been done on mountain bikes. I met some people in 1989 on the Everest Base Camp trek who smuggled their mountain bikes into the park.

Having said that, nowadays mountain bikes really aren't allowed these days for a number of reason including the fact that portions are not ride able and you have to hike a bike, the trails are hiking trails and not built for withstanding the erosion from bikes, it is crowded and some of the trails are narrow so safety is an issue, and I'm sure the trails are much more crowded these days and the thousands of hikers probably would prefer to not share the trail with bikes.

So in short, it is perhaps doable at the right time of year (if trail conditions even allow), but it is not recommended from the perspective of respecting thetrails for their intended use, respecting your fellow trail users, and respecting the natural environment. There are plenty of riding trails where biking is a great way to get around, I'm not sure all sections of one of the most popular hiking trails in the world is the best place take a motorbike.