I believe that you are talking about the Trail of Tears, which is not the only time the Native people were forcibly moved, so I can't be 100% sure. But during the trail of tears the most common causes of death were from cold, hunger, and disease. So if they had not moved in the winter months, the cold factor could have been eliminated.
Moving in the summers instead of winter made the Indians move easier.
Explanation:
The Indian Removal Act, (May 28, 1830), was the first major negotiation between the Government of United States and South Native American tribes. The President of United States signed on this act/ law.
The law commissioned the president to negotiate/ make a deal with the South Native American tribes for the removal of the Mississippi River west of the federal territory in exchange for white settlement of their inherited lands. In this act, many northern tribes were resettled in peace in a western land considered undesirable for a white person.