how do I reduce drafts in a conservatory?

Find Source Of Draughts First

Most likely around edges of openers and doors
then fit a good draught excluder around where req'd
Concerning visibilty
You will be best to put any excluders around frame rebate where op fits into it so the act of closing the op both seals and hides the excluder

With regard to excluder types diy shop bought tend to be a bit flimsy if they are the sponge ones and wont last long at all

See if you can get a local window company to sell you some Kulon get a bit and try it first.
always start half way along top and butt join finish there
Kulon normally fits in a rebate but failing that it can be glued to frame otherwise its a stick on taped type
Hope that helps
Come back if any further assistance req'd

grom-it
November 2008