As the former write has already mentioned the taxis outside of the airport. In Winterthur you can ask at the hotel reception for a taxi service.

Are you aware of the public transport system in Switzerland?
You could also take the train (duration 2h).
1. Bus Basel EuroAirport to Basel station
2. Train Basel station to Zurich mainstation
3. Train Zurich mainstation to Winterthur
Check for schedule on the SBB webpage
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