I would assume that the wearer would also wear fireproof goggles with their balaclava helmet. This would afford them fireproof eye protection when close to a dragon but the ability to have free sight when moving away from them. Hermione and the rest of the Hogwarts gang seem familiar with the use of basic PPE so an experienced dragon trainer like Charlie would also know about it.
‘Oh, it was quite fun, really,’ said Hermione, now putting on
protective goggles. ‘I mean, he drones on about famous ex-pupils a
bit, and he absolutely fawns on McLaggen because he’s so
well-connected, but he gave us some really nice food and he introduced
us to Gwenog Jones.’
Harry Potter and the Half-Blood Prince — CHAPTER FOURTEEN —
Alternatively, the clothing may be imbued with some sort of fireproof magic, in the same way that his brothers' Shield Hats protect the wearer from jinxes.
‘That’s right … well, we thought Shield Hats were a bit of a laugh.
You know, challenge your mate to jinx you while wearing it and watch
his face when the jinx just bounces off. But the Ministry bought five
hundred for all its support staff! And we’re still getting massive
Harry Potter and the Half-Blood Prince - CHAPTER SIX — Draco’s Detour