Yes, lack of wool can be an issue if you have bad weather at lambing. The fineness of the 'skin' is of course one of the things that makes it easy lambing - less friction in the birth canal.
We held off getting a Charollais for several years because of exactly this worry. Then we read an article by another Cumbrian farmer who had switched to a Charollais tup; he said if you got a tup with plenty of wool on his head, his lambs would have a bit more fleece than those of a smooth-headed tup.
We bought an aged tup who had a judge's wig on there and tried him. He was so successful we later bought one of his grandsons - who I sometimes call Carpet Head

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The lambs can be a bit bare, and we do put the plastic macs on the newborns if the weather is cold and wet or predicted to be so. One or two pairs every year are so bare (and the weather unkind) that we bring them in for a couple of days - but this will be just one or two out of 60-100 ewes lambing to the Charollais.
We do always bring in any ewe (whichever tup she's gone to) that looks like lambing overnight if the weather is dreadful, mind, and also any families with newborns who are only a few hours old at dusk.
For us, the ease of lambing and the vigour of the newborn lambs, coupled with the tremendous growth rates and top-bonus-earning conformation are worth the extra work and expense of jacketing the newborns. And whilst we may lose one or two thin-skinned lambs born before dawn on a bad day, I do think that overall we probably lose more Texel x lambs - the Charollais x lambs are so vigourous and up and looking for the teat so quickly, so get the warming colostrum into their bodies before the weather chills them too much. On a cold wet dawn, the more dopey Texel x lambs may not get the necessary warming drink quickly enough, and despite having a warmer coat, can get more chilled than the livelier and greedier Charollais x lambs born at the same time.
If you can check your lambs first thing in the morning, jacket the newborns unless it's sunny and warm, and have any ewes likely to lamb or just lambed on a bad night indoors, then with a woolly-headed Charollais tup you should be fine

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Crossed with Llanwenog you'd get a great carcase

- and lovely fleece for handspinning
