Any major chance of snow in Tasmania in late April?

You cannot guarantee snow but it does occur in April from time to time. Mt Wellington is the most likely spot near Hobart and you might be lucky. If you are going walking in the national park at Cradle Mountain/Lake St Clair be prepared for snow at any time of the year although it is far more likely in winter. There is always a chance of snow but it is not a major chance in April.

the chances on mt wellington are very good
no matter the time of year the weather is so changeable there and snow is possible due to the elevation
when I was young we went on a family christmas holiday from sydney down to hobart... it was cold windy weather and when we went to the top of the mountain we saw snow and yes for us it was the first time

I was snowed on at Cradle Mountain one early January, so there's every chance of a fall in late April.

Mt Wellington Snow