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Can you describe someone as luxurious? As in someone who likes luxurious things?

We're pretty sure you can't, but we don't know what word you'd use. It's not hedonistic, that's different. We're just looking for the word that describes specifically a person, not a thing.

It's a bit like how you can't call someone who likes creamy things creamy.

I believe that I've occasionally seen this done, but I would call it poor writing. rather one might say:

She had luxurious tastes; her closet was full of mink coats and designer outfits.

or

He had luxurious habits; he always flew First Class and stayed in penthouse suites at five-star hotels.

So it is a person's tastes or habits or possessions that are luxurious, not the person directly.

Maybe extravagant is the word you’re looking for. It can refer to someone’s tastes or spending habits or particular large purchases, but also the person themself:

3a : spending much more than necessary

has always been extravagant with her money

bon vivant - a person who devotes themselves to a sociable and luxurious lifestyle.

If you want to sound really cool (and pompous), combine bon vivant with billionaire, gallivanter, and playboy ;)

I believe decadent to be a good fit.

Decadent - noun~ a person who is luxuriously self-indulgent.

https://en.oxforddictionaries.com/definition/decadent

sybarite

noun ( usually lowercase ) a person devoted to luxury and pleasure. an
inhabitant of Sybaris https://www.dictionary.com/browse/sybarite

Epicurean

A person devoted to sensual enjoyment, especially that derived from fine food and drink.
https://en.oxforddictionaries.com/definition/epicurean

Hedonist or Hedonistic person from Hedonism-Hedonism is a school of thought that argues that the pursuit of pleasure and intrinsic goods are the primary or most important goals of human life. A hedonist strives to maximize net pleasure.

You can sometimes use the concept of luxury to describe a person, but it is objectifying; the adjective 'luxurious' is used in the cliche 'luxurious blonde' which usually refers to hair, but can rarely also refer to a person with such hair or Iggy Pop's 'I felt the luxury of her'. This use doesn't mean that the person being described likes luxury, only that some aspect of that person is objectified as a luxury.