Guidance for the industries included in Phase 1 of the re-opening can be found here 5/27/2020

Businesses which are eligible for reopening in Phase 1 MUST REVIEW & ATTEST to the State’s guidelines which pertains to their industry, and must keep a record of that attestation on premises. 

As requested, we have confirmed that wineries are included in Phase 1 under agriculture. Restrictions that are applicable to the industry are as follows: Food and beverage production is allowed to operate statewide, however, food and retail services (e.g. tasting rooms or souvenir stores) are subject to the restrictions that are currently in effect within the region.
We are waiting on confirmation as to within what stage gyms/fitness centers are included. 
Businesses which are not sure if they are part of an industry which is included in Phase 1 can use the State’s reopening lookup tool here to determine if they are permitted to re-open in Phase 1 
If you have any questions, please let me know.
Thank you.
Amy Keyes, Chief of Staff
Suffolk County Executive Steve Bellone
Office: 631-853-4524