Personally, I wouldn't.
Of course, it does depend what sort of parent you are (and what sort of DC DD is!). Personally, I drew up a 'shortlist' of 5 possible comps. We discounted one as the catchment is rigid and expensive. One we (DH or I) visited 'just to be fair' on it; the other 3 were contenders. I found 2 distinct ethoses (ethii??!); 2 felt very 'comprehensive', the third felt just like a GS (I know having been to one!) DS1 would have been fine there but not DS2 and I'm not going to over-complicate my life by having DSs in 2 different schools, unnecessarily! I would have been happy to 'allow' DS to visit either of the 'comp-y' feeling schools in order to make our and his mind up BUT I would have felt the need to carefully tutor him beforehand about not being too swayed by matey teachers, fun-fun-fun activities on Open Day, or where his school friends were going etc etc.
In the end, we chose one more or less for him. We moved into the catchment of the desired comp for DS to go into Y6 of a feeder primary (where 58 of the 60 DC go to said school). He has been well 'schooled' into feeling that this school is 'the best' and I think we've made the right choice. However, our rather less clever DS2 may struggle there (it is fairly academic) BUT, having been in the feeder since Y4 himself, there's no way he'd entertain going to any other school that this comp!
At the end of the day, I personally think it might be a mistake to take a 10 year old on the initial foray. They simply do not have the decision making capabilities or the ability to evaluate, and can be easily swayed by stuff you may not even notice. It can then be hard to persuade a DC that, OK, I know you apparently loved school A and had a fabulous time at Open Day but you're going to school B. Because I saw through the glossy brochure and flannel.
2 of my work mates are going through this at the moment. One wasn't happy with her junior school allocation so 'went purple' as we're calling it. The moment DD spend a taster session at this private, there was no hope for the allocated junior! Cried at the suggestion of it. They are now effectively caught up in paying ££ for the next 9 or 11 years. The other mum told me how the head of one of the local comps was really impressive when she gave a talk at her Y5 DD's primary and how much DD enjoyed her taster day, (Y5, bear in mind). I told my colleague I thought it was presumptuous of the school to offer taster days to Y5's in June, esp as the parents haven't had the opportunity for a shufty, yet! (my friend has effectively 'the choice' of 3 good comps in an expensive, southern city and, imho, is being schmoozed by 'the worst' of them); and that I wouldn't have 'allowed' my DS to go to a Y5 taster day for fear of it colouring his attitude to our final decision, which might be a school he wouldn't have been allowed to spend a day at in Y5 (and I'm not sure I'd want to send my DC to a school that gave up yet more teaching time to advertising!)