A polling team walked for roads covered in thick snow to reach Kuthera and Fatehpur in the Kangra district and Maliyat and Bharmour in the Chamba district of the state.
Thakur, who is an MP from the Hamirpur Lok Sabha seat, is Dhumal's son who was the chief minister of the state twice before losing the office in 2017 after facing a defeat in Sujanpur.
The poll panel issued a notification prohibiting the publication of exit-poll projections in any print and electronic media will be prohibited from 8 am on November 12 and 5 pm on December 5.
Vikramaditya who is a son of former Chief Minister Virbhadra Singh, and also a sitting MLA from Shimla Rural was entrusted by the Congress once again and given a ticket against BJP's Ravi Mehta, AAP's Prem Thakur.
"Himachal will vote for OPS (old pension scheme). Himachal will vote for employment. Himachal will vote for 'Har Ghar Laxmi'. Come, vote in large numbers, and make your valuable contribution for the progress and prosperous future of Himachal," Rahul Gandhi tweeted.
Himachal Pradesh Chief Minister Jairam Thakur cast his vote at Bagshyiad in Mandi's Seraj on Saturday as the voting to elect the new government is underway in the Assembly polls.
Himachal Pradesh Chief Minister Jairam Thakur offered prayers in Mandi district ahead of casting his vote and urged all voters to cast their vote today to "further strengthen democracy".
As the voting began for 68 Assembly seats, Himachal Pradesh Congress chief Pratibha Singh on Saturday said that everyone will cast their vote today and cooperate to form a new government in the state.
Prime Minister Narendra Modi on Saturday appealed to the voters in Himachal Pradesh to participate in the election process in the state and create a new record of voting.