From The New York Times:
When deer are scarce, ticks don’t necessarily become scarce, because they have alternative hosts. Indeed, several recent studies. . . in New York and New Jersey found no correlation between deer and ticks.

Second, ticks and Lyme disease are rare or absent in parts of the United States (the Southeast, most of the Midwest) where deer are abundant.

Third, ticks are only dangerous if they are infected, and deer play no role in infecting ticks. . . . When our group compared the importance of deer, mice, and climate in determining the number of infected ticks over 13 years in southeastern New York State, mice were the winners hands down.