How does 也 work in 宁愿冻死也不穿?
In this sentence 也 should not be understood individually.In Chinese 宁愿...也... is a coordinating conjunction. It means a choose relationship. You choose the option behind 宁愿 and you give up the option behind 也.
I think it seems like rather...than... in English.宁愿冻死也不穿 may be translated to rather be dead than be wearing the long underwear.
More examples about 宁愿...也...could be see in here;
And More examples about coordinating conjunction in Chinese could be see in here