I have a Hamlin Orange tree with oranges that also do not turn orange. They stay green and sometimes have some yellow to them. I know when they are ready by giving them a gentle squeeze. It should feel like a tennis ball more or less. Firm when rested in the hand, but easy to squeeze. Then of course, comes the taste test. If one of them is ready, chances are all the oranges of similar size are ready.
Try a google search for "navel orange harvest" and you should find info on when to harvest them. It's typically a period of 3-4 months.

Thanks! I'm going to check out the links too. I don't expect this to be an ongoing yearly experience, but if it's possible to get a good orange or two off the tree, I think I would like that very much.

When it gets cold at night (below 60 degrees) a ripe orange
turns orange. The problem in regions where it gets too
cold, is freezing. I would let the oranges ripen on the
tree while carefully watching the weather.
If there is going to be a hard freeze,
I would pick one and try to protect the other one
with a blanket and maybe Christmas tree lights.
Here we expect navel oranges to be ripe from October to May.
I think they are best in February.
http://www.ccpp.ucr.edu/variety/376.html

cold temperatures have nothing to do with ripening or coloring up. It is a common misconception because most citrus ripens about the time temps turn cooler but they ripen sooner where temps are warmer. Navel oranges are generally best about December however there are late and early varieties. (Valencia oranges are much later being at their best about Feb. or March.) But, that is for an orange growing region. Since your area is colder, it likely bloomed later and had less heat units through the growing season, so will grow slower with the overall effect of making the fruit ripen later. So,
Watch for freeze. if its going to freeze pick it because the freeze will ruin the fruit. Otherwise, wait a little longer and it will improve. Plan on a nice Christmas present for your self if you haven't had to pick before then. Or even a little later because of being in a cooler climate than standard.

The cold makes them change colour, its the cold triggers the ripening process,as it does the flowering process the next year with the chill hours,

it triggers the plant to act differently,

if not why are oranges in warm places mainly green even when ripe, many florida oranges are used for juice, because of the fact there more of a `green` than an `orange`

cold places=orange, warm places there green

the same with lemons, the verdi crop...(corsica)grown to ripen in the summer they stay green and dont have as much acid as they didnt ripen in the cold, lemons dont need to turn acid as they have a high acid content without the cold, but are better with cold ripening, the same trees produce a winter crop and they turn yellow, in the cold

limes grown in warm places tay green,but they are orange when fully ripe , as are all limes, but they dont ripen if they dont get cold enough , in cold places limes ripen to an orange colour

heat in the summer gives the sweetness , cold gives the flavour and colour change (to most varieties)

I have lemons here, that were 3 inch long in june,they turned pale yellow were leaves touched them earlier in the year and were usable, but there just now turning a real yellow colour as we now have cold weather,
the same with my mandarin tree, all ripening/going orange in the cold outside,
Trees inside the house will not ripen any year unless i leave the heating off at night to allow the temp drop to round 15C from the 30C it is in the day

I just had to post an update on The Orange Tree!

The TV weathernerd said it might freeze last night. Sometimes he's right. We fretted about it and then decided to pick the two oranges.

We shared one for breakfast this morning. Lovely Flavor! Thanks for all the information. Maybe next year we will have THREE oranges, or even more!

But in the meantime, we'll enjoy the blossoms in the Spring.