Wyoming has a cost of living index of 95 relative to the US average of 100. This is close to the national average. Wyoming offers a typical cost structure — housing and expenses track closely to US median.
The 4% safe withdrawal rule suggests a FIRE number of 25x annual expenses. At Wyoming's median income of $65,000, that is $1,625,000. However, if you plan to spend more (or less) than median income in retirement, scale the number accordingly.
Wyoming has no state income tax. Roth conversions, capital gains distributions, and IRA withdrawals all avoid state tax in WY. This makes Wyoming one of the most FIRE-friendly states from a tax perspective.