You can make nature study an "event" - loading everyone in the car with sketch books and pencils and watercolors and guide books. However, it can just be walking around the block and checking out the birds, squirrels, trees and flowers (the bluebonnets have started popping up around here). If you take the same walk throughout the year you can help your kids notice the changes (trees, animal habits, etc.) Just realize that walking with a 2 yo you may not get far - they stop to look at LOTS of things. Enjoy their pace. Often it can be helpful to take a picture if you want to identify something later or draw it at home. I live in an urban area and I think there are at least 6 or 7 different types of trees on my block.
Calendar of Firsts - You can either get, make or just record on your current calendar the first time you see or hear something. We should add our bluebonnets starting up early this year. If you keep it for a few years you can begin to see patterns and look forward to signs of spring (and fall).
Nature Journals - If you are so inclined you can combine nature study and drawing/art. There are lots of resources out there for keeping a nature journal - here are a few:
Laws Guide to Nature Journaling (you can listen to him talk about nature here and here and his series of drawing you tube videos)
Jim Arnosky has a foundational book Drawing from Nature and a series that guides you through the seasons as well.
If you are looking for more guidance check out the Handbook of Nature Study with the Outdoor Hour Challenge.
If you really want to dive in you can flip through Nature Study: A Manual for Teachers and Students. Intended for elementary teachers - it covers the reasoning behind the study, ways to do it and an 8 year course in nature study (year by year and season by season)!
There are also many ideas for nature scavenger hunts, playing nature bingo, etc. I prefer to just enjoy but sometimes a game can spark kids interests.
Many poets have been inspired by nature. There are whole volumes that focus on nature themes.
Of course you can always get field guides to help you identify what you find. Peterson's and Audobon's tend to be good and can often be found at thrift stores. Just make sure you check the region they are from so that the flora and fauna included match up with what you might see in your area.
This is an area I REALLY need to grow in. That's one reason I am linking all of these things so that I can come back and find them. I hope that you delight in the arrival of spring with your family this year.