Today would be a cold day to travel to the Capitol by sled dog - or snowshoes. Rep. Joe Rolette, who served in the Territorial House, the Territorial Council, and in the Senate during the first legislative session, used both modes of travel.
"To attend this session of 1857 he walked the whole distance, about 400 miles, as the snow was too light to permit riding in his dog sled." (Folwell. A History of Minnesota, Volume 1, 1921, p. 386)
"Rolette’s arrival in St. Paul in his gaily decorated dog sled in the winter was one event that marked the opening of the legislative session. On occasion, he made the journey on snowshoes, all 385 miles." (Laken, Neoma. "‘Jolly Joe’ Rolette Jr. a Character, Merry-Maker." Wahpeton and Breckenridge Daily News, September 10, 2010)
More recently, former Rep. Frank Moe traveled by dog sled for eight days from Grand Marais to the Capitol, in order to deliver 13,000 petitions regarding clean water to the governor's office. You can see his dogs in a trailer for a documentary made about Rep. Moe's journey.