Every winter when it gets cold the skin of my fingers develops splits
which bleed and hurt and do not heal unless I put something like
Neutrogena on them for periods longer than overnight. I hate the
messiness of any hand cream which soils any paper I handle.

Does anybody know if this is caused by nutritional deficiency causing
too little blood flow to the extremities and if this can be improved
by vitamins, minerals or anything that can be taken orally?

I used to have this problem. Rather than a nutritional deficiency in
your body, the cause may be a humidity deficiency in your environment.
In the wintertime, indoor air is often extremely dry. This can cause
skin to dry out and crack. Older people, whose skin tends to be
friable, are particularly vulnerable to this.

The best way to prevent fingertip fissures is to humidify your house.
You can buy a humidifier, or just keep big pots of water simmering on
the stove every day.

To help heal my cracked fingertips and keep my skin moist, I used a
product called "Bag Balm" that was originally designed for treating
cows' udders. It's wonderful stuff.

http://www.bagbalm.com/

I've never tried this product, but I've heard that it's very effective
for cracked fingertips:

http://www.vermontcountrystore.com/prdSell.asp?ProdGroupID=218&DeptID=1277&CatID=17262

I have suffered from this same misery for years. While this doesn?t
answer your question, here are the three creams I use for mine and
they seem to do the trick.

CORN HUSKER?S LOTION
http://www.pfizer.com/do/counter/skin/mn_corn_huskers.html
(I use this periodically throughout the day. It absorbs quickly and
isn?t messy - I handle a lot of paper too, so I know what you mean.)

CRACK CREAM (yeah, funny name, but it works!)
http://www.crackcream.com/
(I use this at night and it?s totally absorbed in a few hours)

I also put a small dab of Neosporin or Triple Anti-biotic on a crack
when it becomes really bad. This is the same stuff used in larger
volume on burn victims. It heals my cracks to the point that the wound
is closed and no longer sore in about 24 hours and heals the wound
completely in only a few days.

Good luck
Tutuzdad-ga

OK, vaac-ga: Here is the straight, time-tested remedy for your winter
dry skin problem. First, lotions are mostly useless. I have used this
technique for more than fifty years and it works, so pay attention:
WASH YOUR HANDS IN COLD OR TEPID WATER. Repeat: WASH YOUR HANDS IN
COLD OR TEPID WATER. NEVER EVER WASH YOUR HANDS IN HOT WATER. Here is
the logic involved: Our primitive ancestors, whose genetic makeup we
inherited, never washed or bathed on purpose. No doubt they had a
lovely aroma. If they had to cross a stream or river, the water was
not hot. It is common knowledge that hot water opens pores and leaches
out skin oils. Now, you may think: But my hands won't be clean if I
use cold water. Well, they will be just fine...your skin temperature
will warm the water sufficiently. Once you get used to this, hot water
will feel extremely uncomfortable. I have seen almost miraculous
recovery from severely chapped and split skin by those who tried this.
And best of all, it costs nothing!
  This also applies to hot showers...DON'T !!!

Thank you all for your suggestions which I will try. I will also 
try glycerin slightly diluted with water under plastic gloves. I found 
this to help somewhat but not too much

Plastic gloves are a BAD idea.

This product, which I mentioned earlier has two treatments. One is a
medicated lotion and the other is an oil that is placed in the hands
at night and white cotton gloves (included in the box with the
treatments) are put on over the hands after the oil is applied. Cotton
is the best solution.

CRACK CREAM
http://www.crackcream.com/
(loose fitting cotton gloves are included in the box)


Regards;
tutuzdad-ga