Minato most likely had a nature element which is unrevealed
P.S. Wind cannot be his affinity - since Kakashi mentioned that Minato was unable to infuse his element into Rasengan [Which later on helped Naruto to perfect it and create rasen shuriken] .
I think Minato's chakra nature is fire.. I think I saw him using some fire techniques...
Neither of these statements are accurate.
We already know you can infuse multiple elements into rasengan due to Naruto's STBR
You have never seen Minato use fire jutsu, you were probably just drunk.