ゆきやま is the kun-reading of
雪山. That is,
雪山 are pronounced by Japanese people exactly in the same way. (Well, 雪山 also has a rare on-reading, but you can forget this for now.) If you don't know the reading system of Japanese kanji, please learn it before anything.
But that does not mean you can use whichever you like. Since you are a designer, you know that just producing something grammatically understandable is not enough. Since this is a proper noun, there is usually only one correct way to refer to the name. Visual identity of an organization/product is very important;
iPhone is always
IPHONE. Likewise, if the name of the restaurant is
ゆきやま, you usually cannot use
ユキヤマ (katakana) or
Yuki Yama (English alphabet). See: Why is Toyota typically written in Katakana? (トヨタ)
Rather than asking here, you have to ask your client, and clarify what is the most formal name of the restaurant, and what are the alternative ways to refer to it. Usually your client has his/her own opinion and will tell you which they prefer.
EDIT: Oops, maybe your restaurant is located somewhere outside of Japan and is mainly targeted at non-Japanese people? Is the real name of the restaurant
Yuki Yama, and do you just want to add some Japanese characters as an decoration? If that's the case, and if even the restaurant owner doesn't speak Japanese well, then you may have to choose between
ゆきやま. To the eyes of native Japanese speakers,
雪山 would look relatively authentic and traditional, whereas
ゆきやま would look friendly and casual.