Re: "actively teach" your toddler or just play and let them "learn naturally"?
If I could go back, I would have actively taught. He has just turned 3 and has started preschool, and I've noticed that he doesn't seem to know as much as some of the other children, specifically those that I know are near his age. Today I'm actually going to go pick up notecards that I can make into flash cards so I can work with him at home on colors, shapes, numbers and counting, ABCs and on so much more (full, half full, empty; left, right and more). I've also already picked up a big workbook for preschoolers that helps them work on pre-writing skills and all of the above^.
I'm always explaining things to him. I ask him to point out certain color cars in parking lots when walking to grocery store, I tell him on walks that tree trunks are brown and the leaves are green (and love fall because there's so many more colors!). I point out animals colors and activities like running, jumping, walking, climbing and try to encourage him to tell me what they are doing as well. But, I don't think that's enough.
So with my second son (only 4 months right now) I'm going to keep all these materials I'm making for DS1 and will start actively teaching DS2 whenever he's interested in joining in on our learning fun. DS1 LOVES working on his preschool workbook.