In a well drained raised bed most plants will be perfectly happy in a roughly normal soil with a bit of sand/grit/gravel (including a fair few true alpines). Though the soil might a bit too fertile, which could be a problem in winter.
But your right, most sax's and certainly Androsace's will need a scree mix if you cant provide planting crevices for them.
Youll get away with mossy and the easier silver saxifrages , but for Androsaces and Kabschia saxes youll need a relatively sharp scree.
But i guess im speaking for a (far inferior id imagine) British climate here, and arnt a hugely experienced rock gardener.
Guess youd be best to take my response with a pinch of salt :)

Taiga,
Thank you for your response. I used a regular garden mix soil without any fertilizers. By November here, the plants spread and are fully covering the entire rock garden even over the moss rocks. What is the complications of fertile soil during winter you mentioned? Also, what are the symptoms if the plants of Alpine suffer from non-scree soil? Do they just get bigger and not flower? Or do they slowly die? Colorado winter is dry mostly. I am planning to water the rock garden. Is this something I should be careful about?

I wouldnt be too worried about your soil, but the problem is that they produce lots of loose foliage growth which are generally uncharacteristic and is susceptible to frost damage, rot, aphids, and generally amplifies problems.
If the soil mix isn't gritty enough the lack of drainage and air flow through the roots of the plants will pretty simply stifle growth and cause them to rot. It can be looked at as two different aspects to it , fertility and drainage.
It all depends how the soil's composed, but as you said the plants you listed can be found in borders and really shouldnt be a problem. There probably pretty vigorous in habit anyway, depending on the species.
Dry winters are of course a big bonus for alpines. I dont know if you get snow cover in winter, but for the high altitude species youll want to emulate the dry-ish moisture levels that come from it. In wetter climates, sharp screes are partly used to make up for the climate - so a lot of the true alpines would probably be ok in a normal rock garden mix - which is something like 1 part loam, 1 part coarse sand/grit and 1 part humus/peat , adding 2-5 more parts grit to create a scree.

Watering in winter will be tricky, best keep it to a bare minimum only watering when the soil is close to becoming completely dry.

Hope that rather long winded response helps.

Taiga,

Thank you again. I understand now scree produces less growth and a compact form of plant in general. I also guess then the root goes into deep and therefore needs more air there. That's how they survive in alpine environment. But, if the soil is a regular garden soil, the plant roots system remain near the surface and needs more water during dry winter? We get some snow but mostly the weather is very dry in winter and warm as well. So, I will be very carefully monitoring the water content of this raised bed.

I am nervous to add any alpine species to this bed full of regular garden ground covers. But, I should experiment with some species and see how they grow. The rock garden opened my eyes this year. There are so many plants that I have never known. It is exciting to widen the horizon. If you could recommend some alpines, that will be great. Thanks again.

Im glad my response helped.
Youve pretty much got it down - plants do naturally develop more shallow fibrous root systems in cultivation which leaves them far more prone to drought. But youll still want to encourage the roots down by being sparing with your watering all year around.
As far as the plants are concerned its easy to find yourself spoiled for choice.
The most definitively alpine are cushion formers of Androsace, Saxifraga, Draba, Dionysia and Raoulia.
Pretty much any of the Porphyrion saxes are wonderful cushion, mat and rosette formers if youve got a space with a bit of shade. Then silver saxes have nice foliage, are easier and like full sun here- though dont have quite as elegant flowers. Theres too many species and cultivars to name, but the saxifrage society has a nice website -
http://www.saxifraga.org/plants/saxbase/taxon.asp

The others contain a lot of tricky and un-hardy species, but those that you can get the cultivation right are all pretty much golden. Of the Androsaces id recommend carnea, hedraeantha and sempervivoides as all being pretty easy and reliable even in relatively heavy soil - its a shame the other genera dont have similar species.

Silene acualis is another one of my favorites, quite unlike the other campions. Ranunculus has some pretty idealistic alpine buttercups such as calandrinioides and alpestris .
Im a fan of the dwarf willows as well - theres some really tiny and useful prostrate shrubs such as Salix serpyllifolia and herbacea, as well as x boydii.
Celmisia semi-cordata, Bolax glebaria, Helichrysums (milfordiae, arwea, sessilioides) and Anternnaria are some more that really stand out in my rock garden.
But the end its a all a matter of taste, and i really dont what problems and opportunities youll climate will give you.
But anyway, best of luck with whatever you choose to grow.

taiga,

Thank you so much for the list of plants. Most of them, I have to look it up in my book cause I have no idea what they look like. But, I am very familiar with moss campion (Silene accualis) because I see them all the time at Rocky Mountain's tundra. I will study the list one by one. Here in Colorado, it is finally a winter with snow accumulation.