Thanks Rory. To summarise this so far for anyone reading this thread that is looking into the possibility of changing either the
text cursor and/or the
I-beam.
In Windows 7 to change the text cursor thickness go
Control Panel > Ease of Access Center > Make the Computer Easier to See > Make Things on the Screen Easier to See > Set the Thickness of the Blinking Cursor and then use the numeric drop-down to adjust the text cursor thickness. To test if the change is suitable for your use of Writer click the Apply button and open Writer the text cursor thickness will change immediately when the Apply button is clicked - so just click in a Writer document and you will see the change. When I tested this myself I was surprised to find that it seems not to be a system-wide setting. For example, the cursor thickness changes in Writer and Notepad but not in MS Word, SciTE (script editor) or MS Wordpad. (Interesting to see this change in practice. On a fairly thick setting the text cursor looks pretty well like all text cursors looked in the very early days of computing, a sort of blinking rectangle - took me back a bit.)
In Windows 7 to affect the size, to some extent, and the colour of the I-beam, to some extent, go
Control Panel > Ease of Access Center > Make the Mouse Easier to Use > Mouse Pointers > Change the Color and Size of Mouse Pointers. Then you will see a number of radio-buttons where you can set from a range of alternatives. After making a radio button selection remember to click the Apply the apply button so you can test if the change is one that you are happy with. As far as I can tell this setting does appear to behave in a system-wide fashion - change (of some kind) does show up in all programs that use the mouse pointer and the I-beam. As far as the original issue I raised in this thread goes (the I-beam colour on a "Green 8" document background colour) I found that the "Large White" setting to some extent (but only some) does address the issue. On that setting the I-beam thickens slight and also has a larger vertical size, thus making it easier to see on a "Green 8" document background colour. Some of the other settings produce an I-beam that is so thickened and enlarged that, to my way of thinking, make it pretty clumsy to use.
So in all thanks for the pointers Rory, I found a kind of half-way house for a "Green 8" document background colour because of them. That said I'm not entirely happy with the result. Relative to the Windows default I-beam I find the greater thickness of the I-beam makes it a bit more difficult to use it for positioning it in the text and for highlighting text for cut/copy and paste. Also the increased height of the I-beam is a bit distracting too.
Interestingly, while testing all this out, I tried some other document background colours and found, to my surprise that the text display colour and the colour of the I-beam change automatically to suit (contrast highly) the document background colour being used. In one of them, for example, "Sky Blue 6" the text display colour changes to white and the I-beam and text cursors change to a yellow colour which makes them very easy to see. What that means is that the developers already do know how to change the I-beam colour in Windows but it implies that they haven't considered the colour of the I-beam for all possible document background colours. In essence they already know the solution it just hasn't been applied well for all circumstances. On that basis I would still prefer it if the I-beam colour (and I would now add text cursor colour) were settable by the user.
For now I've changed my document background colour to "Sky Blue 6" and am very happy in the way the text colour, the text cursor colour and the I-beam colour show up well on the screen.

The only problem there seems to be in highlighting text for cut/copy and paste - the highlight barely shows up at all. Ah, well. Seems like the display colours of cursors, text and cut/copy highlighting in combination with user selectable document background colours are a bit of a minefield for coders. Lots of room for good work there - though personally I'd be in favour if all those display colour elements where made selectable by the user, so that they get something that is good contrast to themselves. Having spent a couple of hours toying around with this it really has pointed out to me just how complex this all is when the user has control of document background colour. I'm amazed by how complex it is and the number of different 'elements of' display colour that need to be considered to get it all coordinated well.
In all, as my original issue has to some extent been addressed, I'll mark this thread a Solved - but really there is a lot of work there for coders to improve things if they so wish.