If an opponent uses icicle's effect on me thus turning ozymandias face down, would i be able to use ozymandius's effect next turn or not considering both the finish of icicles effect and ozymandius's effect happen at the end of my turn?
Flip to the back page of any rulebook. There is a specific end of turn procedure.
"End of turn" effects wear off
Then you discard all played cards and draw a new hand
Then you refill the line-up
Finally flip over a new Super Villain if needed.
Icicle would wear off in the first step, Ozymandis is step 2. So Ozymandis appears to be immune to Icicle.