Look at the rules for dark sun concerning dehydration and survival. 3.5 and 4e would be applicable since its in both, officially and unofficially.
The advice I give will be in terms of 4E but feel free to adapt it.
Also, when caulking the wagon, balance would be a factor, so acrobatics or those type of skills,
and for fording the river, maybe athletics if a PC is assisting the wagon across.
Insight or nature for knowing the speed and depth of a river, also wind is a factor as leaving the canvas on when it is windy may be ill advised. Not only that but leaving too early or too late in the year can change how the campaign might progress as the weather changes across the nation and food becomes scarce. I'm sure there will be some wagon fires, wagon circles, broken tongues and clothing that gets lost in the river so be sure to keep accurate records of A) item weight and B) carrying capacity of animals and PCs.
If there is some sort of food/miles based on the three paces, slow, fair, and grueling. and party health based on rations and the number of sets of clothing and days spent resting. In Oregon trail you can usually rest away any sickness or disease as long as you have plenty of clothes and food.
As far as determining who gets sick keep it simple. yeah women may get sick, but if the men let the women have a larger share of the rations then it might be the men, especially if they are doing all the work. Typically little children are sick the most but parents sacrifice to make sure they pull through. I'd stick with a random chance, sure you could figure in the clothes/food/rest equation but you also don't want prevention to be the crux of the game, i would imagine it would be more fun if a random member gets sick but there is a quest that can be undertaken to procure some salve or antidote to save the persons life.
Snakes kill pretty instantly, you have to rest immediately!
I've played way too much Oregon trail but the mechanics are pretty simple to figure out if you just keep fiddling with different settings. To achieve a higher score in the game you must end with all members surviving and more money than you started with. Points are given or taken away based on your starting profession, which you might use as a character background. I'm sure you've thought of most of this stuff but I'm on a roll.
As for modifiers, I would base this on the current supplies. if they made sure to get plenty of caulk then they should get a +2, +5 for expert supplies and whatnot. Skills would be (in the 4E vein) Insight/perception to assess the situation (where to caulk, how much to use) and perhaps a dex/con check for the action of caulking. Just stick with simple modifiers like this.
Use the rules for diseases to decide who gets sick. Target defense = fort, but endurance checks can shrug it off.
Party moral, the pace of the oxen(or other draft animal) is what determines how fast the wagon will go, but if the animals are in poor condition then if pushed too hard they will break things, the wagon or themselves.
*side note, check
http://www.gamefaqs.com/pc/577345-the-oregon-trail/faqs/30964Obviously players with better relations with animals will have an easier time pushing their animals. It is fine to go quickly when there is plenty of grass and water for the oxen, in less desirable conditions they can still move quickly but it is ill advised.
The computer game is pretty much a balancing of supplies and exertion and so the DnD game should reflect that. However a good amount of random things are thrown in to challenge the players, in a DnD game instead of a wagon fire it could be a flyby attack by a dragon. Instead of an ox breaking a leg it could get ripped off by a gremlin.
The trail is hardcore, so you will want to keep things hardcore in your game by not allowing the players certain things. Obviously they cannot carry all the buffalo meet, it expires and there is a load limit. Magic that alters the terrain, such as creating bridges, has to be as difficult to use as caulking the wagon, other wise you would obviously be a wizard and just teleport your family across the trail. Another vote for darksun.
I hope you find this advice helpful and I wish you good luck.
