A Genuine and Moste Authentic Guide: Explorer: A Daring Guide for Young Adventurers (Genuine & Moste Authentic Guides) by Henry Hardcastle, Dugald A. Steer, and Various (Hardcover - Sep 25, 2007 Candlewick Press)
We happened to check out this book from the library (probably because of the snake on the cover) and it has had some fun side effects. It is a really fun, interactive, play-inspiring book. It covers everything you might need to be an explorer, equipment checklists for different areas like jungle vs. desert v. underwater. background research, accounts of historical expeditions. We've been on an exploring kick ever since.
An easy activity for rainy days was exploring our own basement. We worked together to create a map by exploring around a couple of rooms, naming furniture, our ugly old sofa became 'The Striped Mountains'; a chair, 'The Green Hill'; the fireplace was 'Valley of Fire'. When an area was a little dull we put up a colouring page or set out some toys, The wall with an eagle picture became 'Eagle Forrest'; a pile of spilled blocks, 'The Ruins of Lost City'; and our paper mache volcanoes, well they were volcanoes...
Then my explorers set up camp, gathered some equipment like sleeping bags, binoculars and snacks into their tent. While they were busy I drew them a route to take on their map, with important things to find along the way, then I hide various 'treasures' and marked places they should take a rest, etc. I put up a dragon poster under the stairs where I put the final treasure - leftover leprechaun gold and some play jewels.
I highly recommend some indoor exploring for a rainy/cold day activity.
They took it very seriously and worked well together on the different tasks. The set-up was half of the fun, but they still played an hour after they found the treasure and begged to sleep in their camp. They were some very tired explorers.