Your answer is how high is your risk. To lose a division or corps is pretty severe....in those cases I would take immediate action and move closer or directly into supply. If a militia is in the hills next to supply in the winter, I usually wait. If militia survives there are plenty of replacements available. With a corp or division, IMHO, all bets are off and we're running back for supply in most cases. Better to come back another day than to vaporize.
A note. I find the supply system quite elegant its in unyielding stance when it depicts the ACW. To place a quarter of your army in a small section of the East, for instance, for either side, just can't be supported early game for very long and nor should it. Historical reading indicates that both sides suffered war long from the supply needs and how to get them to the troops. McClellan and his successors repeatedly drew up general orders to reduce the size of wagon trains by reducing the baggage train of the officers!
And not only breadth is important, but depth too. You need plenty of supply back home to make sure enough reaches the field.
Large invasions, ala D-Day can't either. Shermans march was to the sea and Union supply not the other way around, from the sea to Atlanta.
The Mississippi is an exception as it provides a supply highway for both sides, within reason.
I hear alot of complaints that the supply chain "reaches me" and thus I shouldn't be effected. Au contraire. The sheer volume of supply that is needed to be concentrated to supply large forces in concentrated areas means some units are prolly gonna go begging unless the commander has had the foresight to preposition through industrialization/carry embedded hard tack and extra ammo. Or had the foresight to target naval ports where ship supply could arrive.
Equally, invasion forces of any size better be prepared for their supply needs with both tactical ship supply/heavy numbers in the Atlantic transport box.
And as the North, you'd be well advised to start early building up a food surplus in the North through industrialization. Late game it will be needed and the USA can't expand well without copious amount of food and ammo throughout his supply grid which spreads thru his acquisitions fairly evenly (unlike how his armies spread). Be prepared for geographic expansion to eat up local supply fast. The CSA equally has to worry about end game food and ammo in the late game. Small shots of industrialization in key areas where Yankees are not likely to look can be the late game difference.
And don't forget bad weather uses supply to keep units from taking damage and thus even more supply must be planned and is required when the weather is bad. At sea, too!
Lastly, industrialization in captured areas for the USA is a great way to expand your supply capacity closer to the front for states to handle larger armies in the field. The deeper into the South the USA goes, the more pronounced it is.
This logistics system is brilliant in its placing heavy logistics considerations before conducting operations. Did you know the average division eats 35 general supply a turn? There are few cities that even produce that, early game!
Many wargamers are just not used to supply in game being this dominant. Each of us is used to playing Patton not Beatle Smith! AACW requires both.
Well done, design team!
Lastly beware the swamps of NC and the bayous of Arkansas and Louisiana. They can be killers.
Bon Chance!
But maybe its too late already 
