The only state that might have gone to the Dixiecrats was Georgia.
Keep in mind that the states that supported Thurmond and Wright were states whose DEMOCRATIC electors were pledged to Thurmond and Wright, and where Truman and Barkley were running as third party candidates. They were also the states with the highest black populations and the fewest areas of Republican strength.
The FAR more likely scenario that would have thrown the election into the House would have been if California and Ohio had narrowly went to Dewey instead of Truman. California (25 EV) went to Truman by 0.44% and Ohio went for Truman 0.24%. This would have resulted in a 242 (D) to 239 (R) to 50 (Dixiecrat) in the EC.
The Democratic Party was such at that time that the Southerners would have been motivated to make a deal to re-elect Truman. They were not in a strong position after the 1948 elections, and Dewey was not a Republican candidate that was appealing to Southerners. It's certainly possible that the Dixiecrats would have bolted to Dewey, but they wouldn't have enjoyed it and Dewey wasn't the kind of Republican that would lead Southern Democrats to leave the Democratic fold.
It should be noted that Dewey didn't campaign in the South. Four years later Dwight Eisenhower actively campaigned in the South and won VA, TN, FL, and TX. I do think that if Dewey had campaigned in VA, TN, and possibly TX, he may have carried those states, but he didn't do that.
I am not really sure about Texas (IIRC, Harry Truman win Texas by over 40%], but Thomas Dewey definitely had a chance to win Virginia, Tennessee, and possibly even Florida in 1948 (I know most polls at the time of the election showed him winning those states). Assuming that he won those states in addition to California (which was very close), then the 1948 election would have went to the House of Representatives.
I am not sure how the House of Representatives would have voted if the 1948 election was deadlocked due to the fact that Harry Truman and Thomas Dewey were both pro-civil rights. At the time, the only Republican who would have done well with the segregationist vote in the South was Douglas MacArthur (who was obviously not a candidate in 1948), as he was strongly opposed to the integration of the military and spoke out against African-American equality in general.
