Carry at least one quart of water with you at all times. If you plan to hike, you should carry at least one gallon of water with you. They can seem tame, but every year people are injured by animals at Grand Canyon National Park. Animals that are fed learn to associate humans with food, get overweight, and suffer during the winter months when free handouts are not readily available. Even small animals like squirrels can bite.
Squirrels can carry rabies and other diseases.
Deer can charge and you can be cut by their hooves. Mountain Lions have been spotted in the North Kaibab National Forest. Keep wildlife wild, do not feed, do not approach, and do not handle. Follow the park speed limit. Be aware that traffic in the park can be very heavy so be patient.