[susan53]

e) We trudged/plodded through the snow.

Not a great deal of difference here.

plod = to walk slowly, with difficulty, but steadily. It's often used with reference to animals

For three days, their stolid oxen had plodded up a blazing valley as flat and featureless as...
The Tortoise plodded on and plodded on..
...donkeys that plodded wearily in a circle (D.H. Lawrence).
Instead, most times T. rex probably plodded along like an elephant

It can also be used metaphorically to mean work slowly and laboriously but steadily on a task, or to get through an experience slowly and laboriously:
16 Sep 2010 – Turkey is still plodding through its EU accession criteria - even though membership remains a long way off.
For 16 years, Toby Jones had plodded though life without exerting himself,
...most of our retailers are plodding through January,...

trudge = again, to walk slowly and laboriously, possibly with the feeling of being very tired or in pain:
He did not try to run. He trudged on, his aching eyes focused straight ahead

It's often used to describe the sensation of walking through something (mud, snow, sand etc) that makes it difficult to move your legs :
...they trudged through the sands of Beirut, with the hot sun striking on their heads.

It seems to be used metaphorically less frequently than plod, but there are some examples :
Few people... can stomach trudging through Proust's work, and who can blame them?

I found one example of them both used together, suggesting that they are often seen as virtual synonyms :
The child's thin legs were plodding. She trudged along slowly, both hands clutching a tired teddy bear.

(Love the tired teddy bear!)