That should be possible. Try (NOT TESTED) something like
<p>Today's minimum temperature was $day.outTemp.min at $day.outTemp.mintime.</p>
<p>The humidity at that time was $current(timestamp=$day.outTemp.mintime.raw, max_delta=600).outHumidity</p>
This works because $current can take a timestamp, which in this case, we set to the time of the temperature minimum. It can also take a "max_delta", which sets how far from the timestamp we are willing to accept a record (10 minutes in this case).
See the documentation for the tag $current for details.