Weather by Season:
If you wish for a sunny week the day before a storm, it will not storm.
When it is raining, you have no need to water your vegetation. It waters all tilled land with or without vegetation. Also increases amount of items in the area (Weed, Grass, Rocks, Lumber, etc.)
In all seasons, there are storms that ruin your crops and obliterate your fields. Also, you cannot exit you house during storms. In winter, you get a field as full of stumps/rocks as in any other season, as though they had not all been squashed down (sort of)by the beginning of winter.
Summer 9 is a storm day.
Storms will occur in summer. Storms fill the land with stumps withered grass, rare grass, rocks and weeds. If you have planted crops or tilled the land there is a chance that the land you have worked on will be affected too. Single squares of planted vegetation will get wiped out in a scattered pattern. It can be very frustrating especially with larger farms.
Normal day. Water crops, walk freely, normal stuff.
No need to water your crops.
You cannot walk around in storms. These obliterate your fields in stumps, rocks, and several other things that normally would randomly appear. You can avoid these by saving every night before bed and resetting if you have a storm.
Snow - No effect
Storms fill the land with stumps withered grass, black and white grass, rocks and weeds. I have noticed it usually affects every square. At least you have no crops to lose. You can avoid these by saving every night before bed and resetting in case of a storm. You cannot go out into your fields in a storm.