I have www.example.com for which I'll be building structured data. The website logo and all other images are on the assets subdomain at subdomain.example.com.
Will structured data references still work even if the assets are not on the same subdomain as the page?
Yes. Structured data is about connecting information across the internet.
Update:
Googles guidelines for logo do not mention any restriction on the location of the logo:
https://developers.google.com/search/docs/data-types/logo
Nor does the underlying specification for logo or url:
https://schema.org/logo https://schema.org/URL
In practice, many sites place their images in a CDN which is often a completely different domain. They have no issue with structured data.
You can also test your structured data using tools like the Rich Results Test. It does not report any issues when URLs form other domains are used.
Will structured data references still work is yes or no. TS doesn't asked about details. However, in case of no i would consider to add some details to achieve the yes. But this wasn't the case here.