The White Stranger is Tommy Oliver's great-great-great-great grandfather and Wild West ancestor. He did not have any ranger powers since the Green Ranger Power Coin was still in Rita's possession and the White Tiger Power Coin had not been created yet, but he still assisted the Wild West Rangers as best he could. The White Stranger is a somewhat reference/parody of The Lone Ranger, a fictional character in Western media.
It is possible that the White Stranger is a descendant of Tom Oliver, Tommy's clone, who was last seen in colonial Angel Grove after traveling to the past. By allowing the clone to live out his life in the past, Tommy may have created his own family line.
The White Stranger's hat has a green stripe to it, perhaps as a historical foreshadowing to Tommy's tenure as the Green Ranger.