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It was probably damaged by the cold. While it can be hardy to zone 6, that's kind of an iffy area. Also, there are different cultivars, some hardier than others. However, since there are some live roots left, it should grow back in time. Recovery from extreme cold can take 2 or 3 years. FYI, here's some material on pampas grass: https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/growing-pampas-grass.htm

The same thing has happened to other people -- apparently the extra harsh winter damaged the roots more on one side than the other. You can cut the dead side down to the ground. Pampas grass is very vigorous, and yours should recover in time. Meantime, there may be some information you can use in this article: https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/growing-pampas-grass.htm

Judging from the number of pampas grass stories like yours that we have been getting from all over the northern part of the country, I would say yes, your plants are suffering from cld damage. Pampas grass is very energetic, though, and I expect if you are patient and continue with your good care practices, your plants will gradually recover. Winter damage can take 2 or 3 years to overcome.

The female plants are the ones with the showier plumes, and normally they are the only ones available for sale. Pampas grass is normally hardy only to zone 7 or 6, so make sure the variety you get is hardy in your area. This article has more information: https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/growing-pampas-grass.htm
You could get more information on plants suitable for your area from the local county extension service. This link will help you find one:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

This article has some answers for you: https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/pampas-grass-removal.htm
Regarding snakes, the vast majority of snakes are harmless to people, and extremely beneficial for your garden, but this article will help with discouraging snakes,if you really want to do that: https://www.gardeningknowhow.com/plant-problems/pests/animals/getting-rid-of-snakes.htm

First, you must have the correct sex. Male plants don't have showy flowers, but since generally only the female are sold in stores, you probably have female plants. This article has several points you can consider in figuring out how to encourage your plant to flower: https://www.gardeningknowhow.com/ornamental/foliage/ornamental-grass/no-plumes-on-ornamental-grass.htm