First of all I only mean books, not the movies please.
To begin with, here is related question - it doesn't reflect Draco's case though. I do not ask what he wears under his robes, I ask if he can be seen walking around dressed like a Muggle somewhere in the books.
So here is what I found on Draco wearing school robes:
He pulled the robes over his head and threw them onto the floor at Madam Malkin's feet... And with that, the pair of them strode out of the shop..
So apparently he was trying his new robes on some causal closes. It would do with a jeans a t-shirt I think, but trying on robes on top of other robes doesn't make much sense. Was Draco doing his shopping on the Diagon Alley in Muggle clothing?!
And later on the train:
To his relief, Malfoy seemed to decide that he had imagined the noise; he pulled on his robes like the others...
He pulled his robes on what? There was Pancy in the compartment and seemed like they changed all together. So were they in Muggle clothes, wearing their robes on those as Ron and Harry apparently do? Or did they have to change their common robes to the school ones?
Now I was thinking - do Pure-blood families arrive to the train station in their wizarding clothes? It seems against the Statute of Wizarding Secrecy, does it mean every year all Pure-bloods have to wear Muggle clothes to take their children to the station? Say, Lucius Malfoy?
We see at the and of The Order of the Phoenix that a whole bunch of adults waiting for Harry at the platform are dressed in Muggle clothing:
There was Mad-Eye Moody, looking quite as sinister with his bowler hat pulled low over his magical eye as he would have done without it, his gnarled hands clutching a long staff, his body wrapped in a voluminous travelling cloak. Tonks stood just behind him, her bright bubble-gum-pink hair gleaming in the sunlight filtering through the dirty glass of the station ceiling, wearing heavily patched jeans and a bright purple T-shirt bearing the legend The Weird Sisters. Next to Tonks was Lupin, his face pale, his hair greying, a long and threadbare overcoat covering a shabby jumper and trousers. At the front of the group stood Mr and Mrs Weasley, dressed in their Muggle best, and Fred and George, who were both wearing brand-new jackets in some lurid green, scaly material.
Though it could be they did it only this time because they intended to talk to the Dursleys. Or not? When Harry first meets the Weasleys on the platform he never notices their clothes, only their talk about Muggles and their owl.
Harry swung round. The speaker was a plump woman who was talking to four boys, all with flaming red hair. each of them was pushing a trunk like Harry's in front of him - and they had an owl. Heart hammering, Harry pushed his cart after them.
Does it mean all wizards obliged to dress as a Muggle when going to the platform and the Malfoys every year appear there in Muggle clothes?
Or Muggle wear is not a big deal for the new generation and Draco does occasionally wear Muggle clothing (like, in Diagon Alley) without considering it to be beneath him?