DD is 3. We've got a birdseed bell outside and like to look to see who comes to visit it. (So far the score is something like birds 2, squirrels 1007).

We put an oversized thermometer outside the dining room window and she's keeping a weather log every morning. She's got a little book she made and we write down the temperature, what the sky looks like, and if anything's falling out of it (rain, snow, etc.).
Making bird feeders out of pine cones, sunflower seed butter (easy to make in a food processor or blender), and bird seed is fun and easy.
You can make a bear cave out of a paper bag, some glue, and cotton balls. Cut a U-shape out of the open end of the bag and staple the edges together, then pull apart some cotton balls and glue them to the top for the "snow." Make a bear puppet to live inside the cave. Goes great with any book about how some animals hibernate in the winter.
Bring some snow and ice inside in clear cups and watch how they turn into water. Magic! Put them back outside overnight and in the morning see how they both turned into ice again, but the snow didn't reform.
Make snow cones. Scoop some fresh snow into a mug and drizzle (real!) maple syrup or orange juice over the top for a sweet treat.