When retires to his summer cabin in the woods, a widowed old hunter must overcome his grief for his wife; but when he finds the trace of an unknown beast, he will venture into the forest to demonstrate himself he is still capable.

The word ‘when’ in a logline usually indicates an inciting incident… the event that sets the story in motion. And while you would never give away an ending in the logline, what sets a story in motion is the event that will be concluded in the final act of the story.

For instance, it isn’t John Wicks’s wife dying that sets the story in motion… It is his dog being killed. His wife dying is a tragic event, but it is when the bad guys kill his dog that he goes on his mission of revenge which will be concluded in the final act.

I have read 3 of your loglines and in all three you have 2 ‘when’ events, but stories only have one inciting incident so there should only be one ‘when’ in your logline.

In this logline, since this is a story about killing an unknown beast, the inciting incident should be when he discovers the beast.
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“When he discovers that an unknown beast is killing local residents, a grief-stricken old hunter must dust off his rifle and pursue the thing before it can kill again.”
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Now in the script the death of his wife and the lead overcoming his grief will be an important part of the story, it is the lead character’s internal journey. But for the logline, you should stick with the main story and hint at the internal struggle that the lead character will go through.

Anyway, the story sounds interesting,
Hope this helped.