As far as I can see, there are two situations where you need to use Supply points during Phase 1 (Start).
Old Man Winter (Card 29)
If [this] is in your Combat Zone, you must pay 1 SP for each deployed army card you want reactivated.
Heavy Tank Battalion [Tiger II] (Card 16)
[This] is not reactivated during the start of your turn unless you pay 3 SP
The English rules state on page 7 "In special occasions, supply cards (0-cost) may be played during the Starting phase."
Clearly, these are the special occasions mentioned in the rules. I have
two three a number of minor questions I just want to clarify.
1) Can the Air Transport Tactic card (19) be used to pay for the SP cost? I assume not since it isn't a Supply card and it would cost a Tactic Point to play (and it appears that you may not play Tactic Points during Phase 1).
2) What about Railway Engineer (Card 26)? Can this be used to pay for the refresh costs? It's not a Supply card but then the SP gain is an effect gained once the card (Railway Engineer) was deployed. I assume the 1 SP would be available, as would the 3 SP if the card was trashed.
3) For example, with Old Man Winter you want to refresh one card (therefore you need to pay 1 SP), what happens if you use a Train Transport (Play Bonus: 3 SP). I assume the 2 "spare" SP carries over to the Tactics, Combat or Reinforcement phases and may be spent later during the turn. Another example, with Heavy Tank Battalion you want to refresh the card but only have 2 Truck Transports, does the 1 "spare" SP carry over.
4) There is another situation where SP carry-over might apply with Panzer Regiment (Card 17) / SS Panzer Regiment (Card 18) during Combat. You need to pay 1 SP to activate the card ability. Can you use (for example) a Train or Truck Transport and get "change". Can you have played Air Transport earlier to pay for the costs. Can you use the SP gained by Railway Engineer? I assume that same applies to this as with Q1-3, so you can. After all, Supply points are "added to your wallet" and can be used during the turn.