Hello Connors,

Monte Baldo is ok in early June, but it is not at all located in the Dolomites! It's a fine mountain located in the Verona Prealps above the Garda Lakes, but its landscape has nothing to do with the Dolomites. The refuges in the Dolomites usually open the third Sunday of June, with some exceptions, so most of them are closed in the period that interests you.
On Monte Baldo there is a cableway starting from Malcesine on the shore of Garda Lake.

Yes, Cresta Croce and the big WW1 cannon are a fine goal near the Lobbia and Caduti Adamello Refuge! I climbed here some years ago. Anyhow a long approach of more than 4 hours is necessary to get to the shelter. Even here, however, we are not in the Dolomites. The group is the Adamello. Very close to the Brenta Dolomites.
I can suggest an area of the Dolomites where huts are comfortable and with quick appoaches and stunning panoramas. Not to be missed!
It's the area around Passo Falzarego. Here it's possible to find some shelters open even in early June.

Yes, it was a fact of epochal significance that still makes nature lovers cry!
Unfortunately, many trees throughout the North-East of Italy - Trentino Alto Adige, Veneto and Friuli Venezia Giulia regions - crashed to the ground like matches due to an extreme weather event at the end of October 2018, never happened before.

The bad weather in the Triveneto area on 26-30 October 2018 is an event that occurred in the north-east of Italy (almost essentially affecting the mountain area) following a strong perturbation of Atlantic origin which led to persistent rains on the region starting from 26 October 2018. To this fact it was added also a very strong hot sirocco wind which, blowing between 100 and 200 km / h for several hours, caused the crash of millions of trees with the consequent destruction of tens of thousands of hectares of alpine forests.
On 29 October the sirocco wind reached 217.3 km / h in Trentino, on the Passo Rolle.