There are two varieties of red clover that are grown – medium red clover (most popular variety) and mammoth red clover (what you're planning on using). According to this PDF from Penn state, the primary difference between the two is that medium red clover is quicker to establish than mammoth and grows back well after it is cut. The following is mostly information for medium red (as that was what was abundantly available) and most of it applies for mammoth, keeping in mind the differences pointed out*.
According to this article from Cornell university, red-clover is a slow growing crop. The seeding times suggested are in Feb/March for frost-seeding and between April to September. Frost-seeding, as Mike mentioned in the comments seems to be a good solution and according to the article he linked to, red clover is one of the easiest to establish.
Perhaps the best solution for you (taking into account the conditions in April and frost in September) is to plant late April/early May, towards the later stages of spring, but as early as possible. This article gives spring seeding a thumbs up:
Spring is the most common time to sow clover. This cover crop is often overseeded into small grain. If mowed at early flowering, it can provide nitrogen and cover through the summer, and even until the following spring.
The pdf from PSU also states:
The preferred time of establishment is in
early spring or early summer, although establishing it after
small grain crops come off is possible. The earlier the red
clover is established, the more benefits it can be expected to
produce the following year.
You should give the section titled "Establishment" in the article a further read, as it has a host of information that is tangentially related to your question.
Whichever variety you use, you should consider planting a nurse crop alongside, to aid the legume while growing by suppressing weeds (important since they're slow growing) and supporting it when it's covered by snow. The article from Cornell article suggests the following for a nurse crop mix:
For a nurse crop, mix 2/3 annual ryegrass with 1/3 medium red clover, sow 20-25 lb/ac.
*In addition, the second article I linked to also warns users not to use mammoth red clover as a cover crop (which is what you're using) although they don't say why. Might be something to look into (perhaps ask locally), and I haven't been able to dig up anything.