caz good luck with the health visitor just nod at her suggestions.
You don't 'have to' put cold water in the bath first, but it is advisable. When you give it a good swish with your hand sometimes there can be a bit of a hot or cold layer right? that is what they are worried about.
My children both have eczema since birth and the number of 'helpful' suggestions could make you scream!! Really what works for them is steroid creams, antihistomines, mositurizer and lots of sleep. So pretty impossible when they were babies.
As to going outside ,well yes sunshine and fresh air is great, but really? the UK in NOV???Tell her you go out to the shops by foot Even going in the buggy to the shops counts as her fresh air tick box.
Also, as a side note,a strong wind and cold air can make my daughters eczema worse, as can getting to hot and sweaty. So a barrier of cream might help in NOV against the cold air.
My son is a climber (his dad rock climbs so might be a bit of DNA) no way would I have put him in a pen/ caged area by him self. He is four now and can climb a standard link fence as high as he likes(and yes if i see him I tell him to stop)..
Good luck and pop over to the eczema boards.
I would say try to listen to the HV there might me a bit of wisdom in there. Remember they are dealing with children in general.
I would take your boy to the shop with the cage/pens watch how much he hates it or see how expensive/impractical they are and then tell her thankyou for the suggestion but the pens are unsuitable for your family, but will try and get out more if she thinks that will help ( then snuggle under the blanket and watch cbeebies).
It is her job to give advise, it is your job to listen and smile, and use the relevant info that might be useful to your family. At the end of the day the advice comes from a good place and she is trying to be helpful. This can be anything from , useful, impractical, irritating and sometimes soul destroying.