Italy's Dolomite ranges

Your train ride, from Munich to Venice, assuming its daytime, should provide as much view of mountains that you need to appreciate them.

I would NOT trade a day in Venice for a day trip to the mountains

Perhaps being here where mountains are nearby gives me a jaded view, but having been to both Venice and the Dolomites, I would not trade a day in Venice for the mtns. It would also be a day devoted more to traveling than actually being there

Dolomites are several hours from Venice by car - with multiple changes if going by train.
For example, almost three hours from Venice to Calalzo (two changes) , then one hour by bus from Calalzo to Cortina. If driving, I would say two hours and half from Venice to Cortina. Not really a feasible day trip.

Cortina d'ampezzo is a 2 hour drive from Venice. I love both places, that's a tough choice as Venice and the lagoons needs at least 3 days.
And the Dolomites need time as well.
If you decide to go the Dolomites way, if you like walking with breathtaking views, go to the Tre cime di lavaredo. You can have a 3 hour walk between the parking, rifugio sapienza and locatelli and back that you will remember a long time.
If not, it will be more a drive in the mountains, or a cable car in Cortina maybe.

I have been to both and say the opposite, I would rather stay in the Dolomite mountains than in Venice but it is good opinions vary.
I do agree though it does not work very well with a day trip, though it could be done.

if you were to do it a car would be required and if staying on the island far from Piazzale Roma it would be much more difficult.
You can make it from the car rental office area in Venice to Cortina D' Amprezzo in a little over 2 hours and that is a very easy drive.
So if you could get there by 7 AM, drive to Cortina reaching it around 9 AM. Have a quick bite, see the town and then drive to Tre Cime Lavaredo you could do some hiking, see the mountains and then drive back to Venice when you are done.

I think this would be a nice day trip, but for someone with plans of staying in Venice for 3 nights I don't recommend it.
3 nights is really only 2 full days and this would be one long full day so leave you with only 1 other full day remaining for Venice. Would somewhat depend on when in June, later the better. If you had 5 nights in Venice I would say this day trip makes sense.

I took an escorted (small tour) day trip into the Dolomites and enjoyed the tour. It was a lot of riding around but there were several stops to get out and stretch legs. Lunch was at a high-alpine agroturismo and we had a lengthy stop in Cortina d'Ampezzo.

Google "Dolomite Day Tours Venice" and you'll see several options.

Thanks so much for all your replies, very helpful. Looks like the Dolamites may have to wait for another time!