Side rant: Crate training is only cruel when people crate the dogs all day and go to work. I have seen this too many times, from otherwise intelligent people. It breaks my heart to see dogs kept in a box prison all day long. When I see this I speak up, even though it is awkward. Many people do not understand that crate training is a means to an end and not a lifestyle for dogs.
OP-I usually take my dogs out back when the weather is good, but when it's really snowy like it has been lately, I clear out a square area in the most convenient spot, even if it is right by my front doorstep. The grass isn't hurt and looks fine in the spring. I wouldn't worry about clearing a long path to a remote area, just do it where it's easy.