Why Wasn't Count Dooku Deformed By The Dark Side?

Because he never immersed himself deeply enough to pay the price. Physical degeneration and permanent yellow eyes came from intense or prolonged use of the dark side, and Count Dooku used it sparingly. He joined the Sith out of disillusionment rather than hunger for power, and he leaned on his lightsaber skill instead of Force powers. His eyes only turned yellow in moments of genuine anger. (Revenge of the Sith; The Clone Wars, "Witches of the Mist"; Star Wars: Knights of the Old Republic II)

What the dark side normally does to a body#

The corruption is well documented. Many dark siders experienced a change in eye pigmentation, their normal colour transforming into luminous sulphuric yellow, blood red or dark orange, usually with fiery red rims around the irises. Deeper transformations turned the whites of the eyes black or reddish, and the skin around them with it. (Star Wars: Knights of the Old Republic II; Revenge of the Sith)

The most severe cases went much further. The user appeared to age rapidly. Skin lost pigmentation and became pale and mottled, veins grew increasingly visible, hair lost its colour, and the voice dropped a few pitches and turned raspy. (Star Wars: Knights of the Old Republic II; Revenge of the Sith)

The key line, though, is about timing. These effects generally progressed with time and continued immersion in the dark side, and would not immediately affect appearance. It is a dosage problem, not a switch that flips the moment you fall. (The Clone Wars, "Witches of the Mist"; Star Wars: The Force Unleashed)

There is a famous exchange on exactly this in the Darth Plagueis novel, where Sidious asks whether he will eventually be physically transformed. Plagueis lists the precedents: King Ommin of Onderon, Darth Sion, Darth Nihilus. He says he cannot promise it will happen, and adds that the power of the dark side is an illness no true Sith would want curing. (Darth Plagueis)

Dooku is the named exception#

The sources single him out directly. Darth Tyranus and Galen Marek did not suffer any of the physical degeneration of the dark side, and their eyes only assumed the yellow hue during moments of anger. (The Clone Wars, "Witches of the Mist"; Star Wars: The Force Unleashed)

That is the whole answer in one sentence, and it is worth noticing what it does not say. Dooku was not immune. The mechanism worked on him exactly as it worked on everyone else. He simply never sustained the exposure long enough for it to stick. When he got genuinely angry, the yellow surfaced. When he calmed down, it went. (The Clone Wars, "Witches of the Mist")

Contrast that with Darth Sidious. Only those who devoted almost all of their being to the dark side had their appearance radically altered, and Sidious was the extreme end of that scale. Even then, his most drastic disfigurement was not a slow decay. It happened during the duel with Mace Windu, when Windu used his own lightsaber to deflect Sidious's Force lightning and the uncontrolled energy radically altered his features. (Revenge of the Sith)

Different Sith showed different symptoms too. Darth Malak got the eye change and a slight pallor and not much else. (Star Wars: Knights of the Old Republic)

Dooku thought he could take the power without the cost#

The reason he used the dark side lightly is written into his character. His break with the Jedi Order came from disillusionment, not appetite. He had strong views about the systemic corruption of the Galactic Republic and grew increasingly disenchanted with the Jedi's inaction, especially after the debacle at Galidraan. He later described staying in the Order for twelve years after that, still believing he could do some good, as being an utter fool. (Jango Fett: Open Seasons; Jedi vs. Sith: The Essential Guide to the Force)

Here is the part that matters. As his discontent grew, Dooku flirted with the belief that the dark side of the Force could be called upon without personal corruption. That is not a footnote. That belief is the operating principle of his whole career as Darth Tyranus. He treated the dark side as a tool he could put down. (Star Wars Roleplaying Game Revised Core Rulebook)

Palpatine, who had been watching him for years, knew exactly what he was working with. He needed someone with Dooku's reputation, skills and financial resources, and he cultivated the grievance rather than the hunger. (Jedi vs. Sith: The Essential Guide to the Force; Darth Plagueis)

The lightsaber did the work instead#

The other half of the answer is technical. Dooku barely needed Force powers because he was one of the best swordsmen alive. (Attack of the Clones; Jedi vs. Sith: The Essential Guide to the Force)

Yoda trained him personally and considered him the most gifted Padawan he had ever seen. Dooku became an accomplished duellist, and in his later years few Jedi Masters were considered equal to his skill with a lightsaber. His form was Makashi, Form II, the style the Jedi invented specifically in response to enemies who wielded lightsabers of their own. Elegant, precise, economical, built entirely around blade-to-blade duelling. (Yoda: Dark Rendezvous; Jedi vs. Sith: The Essential Guide to the Force)

A Makashi master does not need to throw lightning to win a fight. He fences. That measured, mostly calm approach kept Dooku's dark side exposure low across decades. When Yoda finally forced him into a real corner on Geonosis, Dooku opened with Force lightning and hurled machinery around the hangar, and only when that failed did he insist on settling it with lightsabers. Even then, his old master matched him blow for blow, and Dooku had to escape rather than win. (Attack of the Clones)

The upshot#

Dooku's clean face is not a plot hole and it is not special resistance. He was a Sith Lord who kept the dark side at arm's length because he told himself he could, and the physical toll simply tracks the depth of immersion. He had the noble-sounding goal, the aristocratic self-control and the swordsmanship to avoid ever going all in. (Attack of the Clones; Star Wars Roleplaying Game Revised Core Rulebook)

Which is also why he was never going to be the apprentice Sidious actually wanted. That job was always earmarked for Anakin Skywalker, and Dooku found that out the hard way aboard the Invisible Hand. (Revenge of the Sith)