Expenses for exercise related wellness activities can be compensated for within some limits for all companies except sole trader businesses and “Handelsbolag”. Rehab and preventive wellness treatments can be compensated in all businesses within some limits. It has to be the same wellness policy for all the employees of the company. The rules are complex and can’t be summarized in a few paragraphs. In the rules there is a difference treatment of wellness allowance (The company compensates employees for their wellness expenses) and perquisite (Wellness activities directly arranged or paid by the employer). There is no tax free wellness allowance for equipment, such as shoes or tennis rackets. 

https://www.skatteverket.se/privat/skatter/arbeteochinkomst/formaner/personalvardmotionochfriskvard
https://www.skatteverket.se/privat/skatter/arbeteochinkomst/formaner/personalvardmotionochfriskvard/friskvardsaktiviteterao
https://vismaspcs.se/ditt-foretagande/personal/hr-friskvardsbidrag