outdoor cafes in Madrid in late April?

I don't see why not. The tables are outside (at least until the sun goes down) here in Basel already, and we are north of the Alps. It hit 18° here today. And some people say there is no global warming!
According to Wikipedia you can expect average daily maximums of 19° in April and 22° in May in Madrid.

I am in Barcelona right now and there is terrace seating everywhere.

Chani and I had a tasty vegetarian paella at Yuso in Valencia seated outside in mid-March, and I was wishing we had more shade.
Note that smokers rule the outdoor tables, and they do so ruthlessly.

Kind in mind Madrid is a little higher in elevation so it is potentially a little cooler at that time of year. So dress accordingly.

It's part of the Mediterranean way of life... strolling and sitting on a terrace all year around, regardless of the weather. From Oct/Nov until March or so, terraces have heaters: https://media.timeout.com/images/100628653/617/347/image.jpg and some will even offer you one of those blankets like in the airplanes (seriously!)

Thank you all for your replies! Very helpful!

The first time I saw those blankets for use on an outdoor terrace was in Stockholm. They were beautiful red plaid cosy-looking things. We do have heaters in our terraces here in Montreal but red plaid blankets would disappear in a flash!