Warmer back and groin

It's my lower back that usually gets cold, so I wear this vest underneath my other base layers which does the trick. Got a new one on sale from an Ebay seller

https://www.rapha.cc/gb/en/shop/womens-merino-base-layer-sleeveless/product/WBL03SLBLK

Windproofing makes a big difference to tights. I wear the previous incarnation of these: https://galibier.cc/product/mistral2bibs/. Compared to regular tights they do a much better job. I do find my lower legs get a bit sweaty but only notice when I change at the end of the ride, and it's well worth it for less Arctic wedding region.

Sizing is a slight issue for me with those Galibier tights. To start with I found the braces a bit short - though they have stretched nicely - but the legs are a bit long and I have lost a bit of weight. So at 188 cm & 78 kg, inside leg 31 inches on jeans (yay scientific!), I'd get XL rather than XXL if buying again.

I also have the Mistral jacket (normal, not foul weather version) and that's also really good, but if you over-layer below then the cold sweat problem MyBike mentioned happens.

I have a neoprene back support that i sometimes wear. it's for back support rather than insulation but it does do a really good job of keeping your lower back warm when it's cold

I've never heard of a cold back before, even when riding in sub zero temperatures. I would however recommend a good quality pair of thermal Bib tights. They do tend to be thicker and higher on the back than standard summer bib shorts so maybe thats the difference. My current favourite are a pair of Santini, fleece lined and very cosy.

I also wear a back pack keeps me warm and can carry thing for my commute you may also be wearing to much and sweating making you cold

https://www.lapassione.cc/collections/mens-collection/products/psn-deep-...

You could try some big tights like these that offer a bit more protection for the lower back/body. 

4 layers is a heck of a lot, it sounds to me that you might have other problems going on such that you are still feeling the cold, I know it was a bit parky yesterday, (I was into work for 7:45 so not mega early but I'm northern home counties) but even just going into work a few miles away I'd worked up a sweaty head and hot body with a summer jersey/arm warmers, Polaris windproof and a mountain Warehouse softshell though I used my Showers Pass today.

Helly Hansen Freeze is a good bottom layer IME, if you're not working your body fairly hard then you're going to be less warm all round.

The perceived wisdom is that the back is the last place that should be getting cold - which is why most cycling kit will have less protection at the back to aid the escape of heat. Windproofing (and therefore the warmest) areas are at the front and on the arms as these are the areas hit by the wind. I have two dhb winter tops that have the same thickness of fleece on the back as they do on the front, but only the front has windproofing.

Are you sure you're not wearing too much, and the resultant sweat is cooling you down too much? Four layers does sound a lot - I was out yesterday am in temps around 0c, and three layers was bordering on being too warm (then again, everyone is different).

As for the groin, can you just wear some baggy(ish) shorts over the top of your tights? I must admit this is one area that I find the chill gets in on the coldest days, especially when I've gotten out of the saddle going uphill and exposed the 'undercarriage' to the air.

I know it's very rarely the done thing, but how about a rucksac.  I wear a courier bag all the time and my back is always toasty, sweaty, but toasty.