Depends on the plant. Given our forecast is for 8 inches of snow over the next two days, though, I would say now is too early for just about everything. You might want to do some googling to check on how cold hardy your different seedlings are, or you could post a list here for folks to chime in about. Best wishes in managing your jungle!

When I was using a protable plastic greenhouse I usually could start using it sometime in April, late March some years but this isn't one of those years.

That said, I was also prepared to run a milkhouse heater in there on the occasion the forcast was to dip below freezing.
You can get a portable digital thermometer pretty cheaply that will record high and low temp for the day (need to clear once a day as well). Using one of these you can monitor the temp in the plastic greenhouse before putting any seedlings out in it. Once the temps seem reasonable (not dipping below 35-40 at night, or reaching over 90-100 during the day) then you can move seedlings out.

In addition to watching the night time lows, I found I had to make sure to open the ventilation in the greenhouse in the morning if the forcast was for a sunny day (I work and am not home all day). Temps would get quite warm in there and you need to worry about your seedlings frying.

Typically I'm always paranoid to move everything out at once, so I'll pick a few of each variety of what I have and set those out. If they do well after 3-5 days then I move the whole batch out.

I hope that helps some. I loved my 6 X 8 portable plastic greenhouse. I'd still have it too, if my DH hadn't built me a permanent structure.