The peak season is autumn: late September through mid-October, when the maples around Hubbard Park and across the Winooski valley turn red, orange, and yellow. Rooms book out months ahead; weekday visits and early-October dates are the easier window. Summer is mild and green, with long days and a strong concert programme on the State House lawn. Winter is properly cold (sub-zero Fahrenheit nights are normal) but Montpelier is a good base for skiing at Stowe, Mad River Glen, and Sugarbush, and the cross-country trails in Hubbard Park are excellent. Spring is mud season — locals do not recommend visiting in April unless you have come for sugaring.
The Vermont legislature sits from January to May; downtown is busiest on weekdays in that window.