At Lake Alpine Recreation Area in Arnold, California you will find several trails that actually converge into one large trail, depending on how far you want to go and what you want to see. The trails vary in difficulty, but they all allow dogs as long as they are kept on-leash at all times. The trailhead for the Hike Around the Lake trail starts at the end of the park road by Pine Marten Campground.
From the trailhead, the Hike Around the Lake will take you four miles around the lake. The path will take you along the shores of the lake, some of it muddy and some of it rocky, over the Silver Creek, and past several campgrounds. You'll see a lot of wildlife and wildflowers along this path, and it is shaded by giant oaks and pine trees. There are a few picnic areas and portable restrooms along the path by the campgrounds for your convenience. The other trails are not marked well, and are all-natural dirt paths, so you will need a map that you can get online or at the Lake Alpine campground or resort.
The Emigrant Trail is a short trail of about two miles that takes you from the lake trail to Bear Valley or up Osborn Hill to another campground area. You can also hike to Highway 4 and head back to the lower end of the lake, or to Inspiration Point Trail. This trail is just over a mile and is mostly uphill about 600 feet to the summit where you can see the lake from above. These two trails are both just offshoots of the Hike Around the Lake trail, and there may also be other unofficial paths that campers and hikers have worn down that will take you to some good fishing spots if you would like to try your luck.
All of the sections of these trails are shaded, and composed of natural dirt with some rocks and big boulders. You will undoubtedly see some flashes of color among the greenery of the native wildflowers. Make sure to pick up after yourself and your pooch, and bring water. You may want to come back at other times of the year as the trails and foliage change with the seasons.