Living in the northeast, we see a few snow storms a year.

I currently have the OEM pirelli summer tires on my 16 Conti GT speed.
Right rear tire has a nail in it and I plan on replacing it.

The left rear tire has 6/32. I understand the new tire will come with 10/32 tread.
Is it better to get two new rear tires due to the difference in tread depth?

also is it worth swapping summer and winter tires twice a year or switching to all seasons?

Thanks for the suggestions