So, basically 'look like a vampire' includes 'look like a normal healthy version of your character'. At least it should.
That part I can get behind. I wish vampirism didn't wash out body markings quite so much. I can understand making them fade a bit, but the problem is they fade so much that all Khajiit and Argonians pretty much look the same at stage four.
Firstly, it's pointless, as was said. Secondly, stage 1 is not 'a normal healthy version of your character' and still should look rather obviously vampiric to all NPCs who have a bare minimum knowledge of vampires. Only completely unaware should be fooled by 'it's just a cold' excuse. But there are dozens or even hundreds of knowledgeable and experienced characters that know a lot about vamps, like most of the Mages and Fighters guilds, some nobles and military, definitely all of the most powerful mages and sorcerers like Fyr and Tharn, adventurers and the Undaunted, some of thieves and assassins. There's a quest in Grahwood where vampire hunters can't see a vamp in front of them at all (and they weren't completely stupid or inexperienced)!