Not really. First sentence is about snow- only snow. Second sentence applies two attributes to the winter: hard and snowy. It could be a hard winter without being snowy or it could be snowy but not particularly hard. There should be a comma between hard and snowy.
Since we can only meaningfully comment on weather after it happens, it should be in the past tense: It has been a hard, snowy winter (if it is still winter) OR It was a hard, snowy winter if the winter in question is now over.
If the intention is to imply that there is a lot of snow, I prefer the word heavy: It has been a winter of heavy snow. We've had a lot of heavy snows this winter. It has snowed heavily this winter. We've had heavy snow many times this winter.
Hard snow implies high wind (or other weather factors) in addition to snowfall.
- For Teachers