Hi Sally. I'm glad you believe your boss thought he was being constructive - and like I said earlier, I think it's the delivery of this feedback that has been clumsy and hurtful, rather than the feedback itself iyswim. For that reason, I have every sympathy with your reaction - it hit a nerve as you say - but your boss wouldn't have been aware that this was your achilles heel.
I'm assuming that you have staff yourself - and as you say, your new role will involve you engaging and influencing people who are not your direct reports, so the way you come across to people is important to getting the job done and the business overall. In this respect, I think the feedback itself is fair and possibly insightful. What I want you to do though is to remember that he didn't say you were "cold and unapproachable" - just that you "come across" that way. It's always much more helpful to describe perceptions and behaviour, rather than criticise someone's personality.
So, remember, you are not cold and unapproachable - but it could be that you give that impression sometimes.
I would enter the meeting very calmly and try to have some humour about the situation too. If you know him well enough, give HIM some feedback on his feedback skills! However, before you do that, do ask him for some specific examples of when he has gained that impression. Very often, when people are perceived as being cold, it's because they don't look up from their work when people approach them. Usually this is because they are so absorbed in what they are doing, but to the person approaching, it makes them want to turn on their heels! Hence they feel you are being unapproachable.
Next, say that you realise that this impression can be damaging to your working relationships and that you would like some help with that. This could be the 360 degree stuff I mentioned earlier, or a coaching programme - perhaps do your own research prior to the meeting, find out costs and ask him to support you.
In answer to other posters, I suspect what he said to you will not be written down anywhere on the appraisal. In FTSE companies, appraisals are usually more objectives and goal orientated, but do tell us otherwise if that's not the case.
And maybe he wouldn't have said the same to a man, but I've also known men who aren't "clubbable" (i.e not interested in sport, cars and watches) given far worse feedback than this. They are treated like social pariahs by "alpha" (or neanderthal) males - and in my experience, get sidelined far more than assertive females.