Could be an electrical issue with the fuel pump. That access port is underneath the rear seats - could be a damaged wire that is shorting to ground due to the extra cold/moisture.
Could also be physical damage on the coil packs - might be a good idea to give them quick look over, see if there are any cracks - hit them with some WD-40 (wipe them down afterwards) to help displace any moisture. See if that helps with the starting issue.
Don't forget the plug wires - sometimes they can have cracks / very slight checking on the length of the wire that can bleed off spark power. Same deal - wipe them down, check for damage. Might try adding a little dielectric grease to the boots to help chase off water.
2002 Toyota Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Toyota Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Toyota Matrix XRS, 2.4L 2AZ-FE VVT-i
2009 Toyota RAV4 Limited, 2.5L 2AR-FE Dual VVT-i