I believe I can give you the Yankee answer. If anyone supported the war of the rebellion they fell out of grace. The radicals controlled much of the government directly after the war. However those former Confederates who had served in the Mexican War later received their Federal pensions for the Mexican War.

Interestingly some galvanized Yankees from Mississippi would receive a Federal Pension for a while but because they also fought for the rebellion some of them were denied their Federal pension. This happened to a soldier in the 3rd Mississippi Infantry who turned Yankee in early April of 1865 and would join the 5th United States Volunteer Infantry Regiment. When he was ask on his pension application if he served in the Confederate Army to aid the rebellion he wrote back. And I'll paraphrase "When you enlisted me I was a Confederate prisoner of war at Camp Chase. You knew I was a Confederate and were glad to enlist my services and now you deny me a Federal pension because I had been a Confederate. I was honorably mustered out of service at Fort Kearney in 1866 and when I need money you deny me my rightful pension. Senator George has received his Mexican War pension and he was Confederate General and Senator yet you deny me."

The galvanized Yankee did receive a pension but a few years later it was revoked on the basis he had been a Confederate soldier and aided the Confederacy. This information was found on his pension records at the NARA in DC.