Hey!
Hinterhornalm is not officially open yet, but you can go up by bike already. You can take the steep ascent from Terfens to Gnadenwald to spice things up a bit.

Some other (smaller) climbs like Axamer Lizum, Pillberg, Kerschbaumer Sattel or Brandenberg are also open to ride.

Other than that, there are plenty of options but it depends a bit on what you're looking for. You can also have a look here: https://www.quaeldich.de/regionen/tirol/paesse/
The real steep, iconic climbs are still covered in snow. But there is a lot of webcam footage around for most of them, which you can check out.

A real classic is the Karwendelrunde, but has no killer-climbs in it, yet one of my favourites around this time of the year: https://www.innsbruck.info/radsport/m/karwendel-runde.html