I have a few ideas
Seasons
Spring
A time of growth after the winter period could be be represented by plants starting to bud, tree's starting to get there leaves back and maybe have more rain.
Summer
Hotter longer day's (more stamina loss when outdoors during the day), tree's have recovered there leaves.
Autumn
Leaves have turned red and the weather has cooled.
Winter
Snow covers the ground, trees have lost there leaves and when outdoors or away from a fire you need to eat more because of the cold.
Certain animals would be hibernating in there lairs like bears so you would not meet them.
You would also have to store food for the winter as crops and wild fruits would not be available.
You could have plant sowing and harvest correspond to the correct season.
Maybe have a 6 hour period per season.
Im not to sure about the lenght of the seasons.
Fishing
Have stocks of fish in certain area's, there are only so many fish in a lake and they are harder to catch when they are fewer in number.
If you have a ocean in the game you could have salt water fish and fresh water fish.
Another idea is to have salmon that move from the ocean to the rivers and up into the lakes, during this time it would be alot easier to catch them in any of the rivers leading to the lakes.
Worship/Religion
You could have it so you could make sacrifices to your ancestor on alters in goods and food.
After death you could have your friends bury you they could put tools and other items into your grave these would have some effect on your next character in the same way as offering sacrifices to your ancestors.
Food decay/Storage
Food that is not stored in a container should rot thus encouraging people to use baskets and pots.
Tools
After a number of uses tools should degrade depending on the type of material it is made from a stone axe should degrade much quicker then a Iron one.
This would make it so blacksmith's and carpenter's would have a vital role in a town.
Misc
Limiting the number of branches and bark one can take from a tree until they grow back.
More types of wild fruits such as black berries.