Not really related to the make-up issue, but please be aware that you are going to be damaging your relationship with your daughter through the way you handle situations like this - you say I scrubbed it off and put my hair up in a ponytail, bunged on jeans, jumper and boots and went to the theatre with them —wearing my dog walking coat to make a point— now I know it’s not DD’s fault and I have told her this - well, if it's not her fault, why "punish" her by going out dressed like a scruffbag to make a point? Your choice to dress like that was directly related to her comment. Ergo, her fault. It's a totally passive aggressive way of dealing it, and your actions are in direct conflict with your words, which is really confusing for the child in this picture.
As previous posters have said, it depends on the conversation, but as a parent you should have either a) not set your child up in this conversation where you asked her to judge your appearance or b) having got into this conversation, take that opportunity to talk to your child about how what she said could hurt and different ways that she might like to say things that could be kinder. It'll be a good skill for her to develop so she doesn't say similarly tactless things should she find herself in similar situations with friends etc.
Secondly, you are a key role model for your daughter, so talking negatively about your own appearance is going to shape her concerns and fears about her own. She's going to get enough messages from society about people's value lying solely in their appearance, and you need to build your own confidence and self-belief that you have value beyond what you look like, so you can be a healthier role model in that respect. Depending on where this self-loathing is coming from (I am sure you're not "ugly" - perhaps not "conventionally beautiful", but ugly, no), you might want to consider some therapy to unpick the root causes, so you can be a positive role model for your child to help support her own self-esteem to not be overly contingent upon her looks. It is hard though, and getting harder with social media and filtered selfies reinforcing quite narrow definitions of "beauty". 