Okay… things I think will not happen… Gordon will not meet Chell. There will be no romance between Gordon and Alyx. It won’t be a simple matter of taking the helicopter. Valve won’t decide to take control from the player unless it’s right before the first instances of the game, like at the beginning of EP1. Also, Breen is dead. He’s gone, he’s done for, he died in the explosion. Get over it, people.
As for Episode 3/HL3:
Let’s not forget that the Combine are aware of White Forest- if Advisors are there then there must be troops and forces there as well. There will probably be some kind of evacuation of White Forest as Combine forces advance. It’s no massive army- it’s whatever forces were accompanying the Advisors. (Enough to be a threat at the time) Scientists like Kleiner and Magnusson will be top priority (and Alyx and Gordon too, obviously). The advisors are probably rushing back to the combine’s current temporary stronghold, or wherever they are safe, since Dog almost killed them.
I do think a “dream” sequence is in order- we see Alyx crying over Eli, and then a fade to black- G-Man might say a few words to us about the Borealis, or overall situation, or something (we can’t really predict what he would say right now). The game will probably start right after that (if the dream sequence even takes place) with Alyx waking Gordon up. We are in the same room we were at the end of episode 2. Gordon was probably asleep for 1-2 minutes (well needed rest, don’t you think?) while Alyx put a blanket or tarp or something on top of Eli to cover him as there is no time for a proper burial.
We see the helicopter- maybe it’s a little damaged after the Advisors killed Eli, or perhaps it’s still flyable. Either way, it doesn’t matter since they’d probably get shot down by advancing Combine forces. Unfortunately they will need to find another way to the Borealis. Alyx will say a word or two about Eli- and then will remark that even though she would like to have some sort of funeral they have to leave before the Combine find them. She’s really distressed and it shows- her dad just died and she can’t even bury him.
As I said, an evacuation is underway. They go back the way the came, or maybe to some other area of the base not yet seen. At this point, I see one of two things. Either:
We meet up with a rebel somewhere, who tells us that the scientists are being evacuated and will be safe. He says he’s here to escort Gordon, Alyx and Eli, and Alyx tells him about Eli. He expresses his regrets, and walks them through some unseen areas of the base. We are taken to a vehicle, and told to meet up with some rebels somewhere before arriving at another base further up north. Gordon and Alyx leave the base.
Or:
We meet up with Kleiner and Magnusson, who are about to evacuate- Alyx tells them about Eli, they express regrets, and mention that they will discuss their plan later. They mention another base up north, and that rebels are waiting to guide them away from White Forest. Then they split up, and a rebel takes them through an unseen part of the base to some vehicles.
At this point, we drive along some kind of road or path away from white forest with the usual puzzles, etc. At one point, Alyx and Gordon reach some kind of small rebel checkpoint- and eventually they reach a base further up north. They have a ways to go to the artic, but some time to prepare without the disturbance of the Combine. On the way to the base, things gradually get colder, and we start to enter a tundra area. By the time we reach the base it is snowing.
Now, it gets harder to predict things at this point, but they probably will talk to Dr. Kleiner at the northern base. He will tell us more about the Borealis, and there will be a discussion (why did Eli not approve, etc.). After this, Alyx will leave for a few minutes to think things over (remember she’s human, and Valve wants her to be more than a “bullet spitting robot” 
), and Kleiner will tell Gordon some more information (whatever he knows about the G-Man, if anything- maybe some more info about Black Mesa, or the overall story, etc.) We might even talk to Barney during this time.
Overall, the northern base will serve as a good point for some catching up. It will not be as big as White forest- perhaps it goes deeper underground.
So, this would be approximately the first half of the game if it’s episode 3, and the first third (or quarter?) if it’s HL3. The second half (if episode 3) or quarter would be making your way to the Artic, somehow. There might be some new modes of transportation here we have not yet seen. There’s not much more I can say at this point, but I suppose it would involve the usual speculation on the Borealis. They certainly won’t be going to the Combine’s home world so soon.
