Right, by searching online trees and Canadian Census it would appear that he was married to a Helen (or Ellen) S. Corbett and that they had 3 children:
William Wallace Adams b.2/2/1866 Dakota, Nebraska
Lizzie Adams bc.1869 Ontario
Robert bc.1878 Ontario
The 1901 census states Thomas was born 1/1/1812 but 2 earlier census suggest ca.1815!
He died 28/7/1903 in Vespra, Simcoe, Ontario - his headstone states born 1/1/1811.
NONE of the records available online show him as Thomas William Adams - just Thomas Adams.
There are 4 trees on Ancestry and all 4 show him to be the Thomas Ward Adams, bp.12/1/1811 St. Marys, Woodbridge, son of William Adams and Margaret Ward.
HOWEVER, Thomas Adams aged 3 (b.1811) was buried 12/8/1814 St. Marys, Woodbridge - this would appear to be the child of William and Margaret so not the Thomas who ended up in Canada.
This begs the obvious question - where has the information come from that states Thomas Adams in Canada actually came from Woodbridge, Suffolk? As his headstone in Canada states he was born 1/1/1811 has someone just assumed the baptism on 12/1/1811 in Woodbridge is him because the date 'fit's' which others have duly accepted and copied?
The fact that the Thomas Adams bp.1811 Woodbridge does not appear in 1841/1851/1861 UK census - your man not arriving in the US until 1860's - would concur with the burial of 3yr old Thomas Adams in 1814 at Woodbridge. Another Thomas Adams was bp.6/9/1815 St. Marys, Woodbridge, son of an Edward Adams and Mary Amos - this Thomas can't be your man either because he died and was buried in 1834.
Has his marriage to Helen S. Corbett been traced? It's possible that the marriage certificate might have added details about Thomas.
Certainly, the only 2 Thomas' baptised at St. Mary's Woodbridge near the relative time given for your Thomas' birth i.e. 1811 both died - one at aged 3 in 1814, and the other aged 19 in 1834.
Is there definite proof that your Thomas came from Woodbridge?
Annette