The law applies to you and your business, not to your hosting provider. Therefore it is your own responsibility to ensure that any cookies your website drops fall within the new regulations.
Some cookies are excepted if they are necessary for your website to function correctly, for example, any cookies used to remember goods the user wishes to purchase from your website are admissible. Cookies that are not necessary are not excepted and will require the user's acceptance. For example, first and third party advertising cookies.
If you are unsure what cookies your site drops, or how to check your own cookies, then there are some options available to you. For example, there are third party cookie checkers:
There are also tools that allow you to add a consent panel to your website, giving users the option of allowing cookies, for example Wolf Software's Jpecr Package.
