According to Bible records, my 3rd-great-grandmother Anna "Ann" Walker was born on February 28, 1842, and married my 3rd-great-grandfather John Bennet Winters on October 10, 1859 in Tonawanda, Erie County, New York. According to the 1860 and 1870 United States censuses, Ann was born in Ireland. The family had moved to Chicago, Illinois by the mid-1860s. Ann died in Illinois on September 19, 1872 (this information also came from Bible records).
I looked at the New York State Census, 1855, and I think I may have found Ann. I found a widow named Ann Walker and her family in Seneca, Ontario County, New York. Ann was 44 and was born in Ireland, and had been a resident of the town for 9 years. Her children were James, age 18, born in Ireland; Ann, age 13, born in Ireland; William, age 4, born in Ontario County; and Dora, age 4, born in Ontario County. The same family appears to have been enumerated again in 1855 in Buffalo, Erie County, New York. They had lived in the city for one month. The family consisted of Ann Walker, age 43, born in Ireland, widowed; son James, age 18, born in Ireland; daughter Ann, age 12, born in Ireland; daughter Dora, age 3, born in Canada; and son William, age 3, born in Canada. In the 1870 United States census, I found Ann Walker, age 49, born in Ireland; James, age 22, born in Ireland; and twins Dorah and William Walker, age 8, born in Canada. Daughter Ann is not in the household. Ann Winters was with her husband John in Tonawanda, Erie County, New York, and according to the census, they were married within the year.
Since Ann was only 17 when she married John Bennet Winters, it seems likely that she emigrated from Ireland with family, probably during or shortly after the Great Famine. Ann, daughter of Ann Walker, seems like a good candidate. I am hoping to find more evidence.