Summer (June through August) is the obvious choice: the Snowy Range Road is open, fishing is excellent, and hiking trails are accessible. But Saratoga in winter has a particular magic that is harder to find elsewhere. Soaking in the Hot Pool at 43°C while snow falls is the iconic Saratoga experience, and it is worth planning a trip around.
Ice fishing on the North Platte runs January and February. Cross-country skiing and snowshoeing are good throughout winter in the surrounding country. The Snowy Range Road closes with the first heavy snow and does not reopen until around Memorial Day.
Spring and autumn are shoulder seasons: quieter, cooler, and less visited. Autumn is especially good for fishing — water temperatures settle and the cottonwoods along the river turn gold.