Fossilization isn't the only way for a creature to be preserved. Natural preservatives such as ice, sand, and peat bogs have kept the bodies of both animals and people from decaying, making them records of ancient times in a similar way as fossils.
Extinct mammoths and mastodons belong to the same order as the two living elephant species: Proboscidea. Mammoth bodies have been found in Siberia and other places, frozen and so well preserved that in at least one instance their meat was given to sled dogs to eat! The ice that the mammoths were 'buried' in worked like a giant freezer, effectively keeping the bodies from decaying. Mammoths most likely were not able to survive entirely in a land of snow and ice, based on the evidence of living elephants, who have to eat a huge amount of plants every day in order to stay alive. Mammoths were about the size of an Indian elephant at the largest, and some were smaller. (Male Indian elephants are about 9' at shoulder height and weigh five tons; females are smaller.)
People can also be preserved, as mummies. In Egypt, the first mummies were accidental--bodies buried in hot, dry sand naturally mummified. Later, embalmers removed a person's organs immediately after death, so that the body would not begin to decay. They washed the body and then dried it out with a salt called natron. (Natron is a mixture of sodium bicarbonate--baking soda--and sodium carbonate.) After the body was dry, it was anointed with scented oils and then covered with resin for further preservation. For the final touch, the body was wrapped in cloths, placed in a sarcophagus, and then sealed in a tomb.
Not all mummies were preserved on purpose the way ancient Egyptians were, though. The 'Bog People', found in locations throughout Europe, are well-preserved bodies that did not decay, due to properties of the peat bogs they were found in. The sphagnum moss in the bogs works as an antibacterial, and the bog itself is an anaerobic environment which helps prevent decay and 'tans' the bodies of the Bog People like leather. Some of the bodies are thousands of years old, and many still had clothes and other personal effects with their bodies when they were found.
You can demonstrate how mummification works, using some fruit or other food and a bag of salt. First, show your children how grapes and plums look compared to raisins and prunes. The dehydration process in Egyptian mummification caused somewhat similar results! Pick out the kind of fruit that you want to 'mummify' and put in a container, then cover it with salt. You'll need to let the fruit sit for two or more weeks before it's dried all the way. If you'd like to compare mummification to the freeze method, put one of the same kind of fruit in the freezer for several days and then compare it to the salt-dried fruit. How are they different? Which seems most helpful for scientific study?