Estonia has 1 festival in this guide, spread across 1 city. They run in August, and festival-day temperatures range from 21°C (70°F) to 21°C (70°F), with nights down to 12°C (54°F). That range is the reason there is no single "Estonia festival outfit". The answer changes by month and by site.
Conditions are moderate across the board, so the day-to-night temperature drop is the thing to plan for rather than the weather itself.
The ground matters as much as the sky. Every festival here is on forest, which puts broken-in trainers or a low boot at the top of the list for most of these events. 1 of the 1 has camping on site, so outfits have to survive living in a bag on the ground for several days.
Stylistically the crowd here leans forest, indie, camping and cottagecore. Intsikurmu is the largest of them at around 6,000 people, and it sets the tone the smaller ones react to. None of that is a dress code. It is what you will see, which is worth knowing if you would rather blend in or deliberately not.