I wear a Castelli Alpha Wind Jersey with nothing but an SS synthetic baselayer underneath in temperatures of 2-3'c and I have been absolutely fine. I have also been caught out by the odd shower and providing that its not a heavy downpour, the jersey can pretty much shake most of it off.
Ive even worn it in quite a persistent though not very heavy downpour and even though the surface of the jacket was pretty wet, the rain never got inside - The sleeves on the other hand did get a little wet. but air drying it made sure it was ready to wear again the very next day.
Sportful have a similar product called the 'Fiandre Light No-Rain Long Sleeve Top' It might be pricey but its worth the money imo.
your millage may vary though 2-3c is fine for me as i run quite hot. With a base layer on, The cold is only ever a problem if you stop for a fair amount of time. If you are of medium or large build though you can easily buy a size bigger to fit extra layers underneath If that is what you wish.
I have an Louis Garneau Gilet here that i bought for cheap from
Evans that i have never worn even once. though I might carry it just as an extra layer for the shoreham-on-sea FNRttC