The land was predominantly a single continent at creation. There may have been massive lakes, significant water courses, the presence of fixed and floating islands. Various ecosystems existed based on location such as latitude, altitude and proximity to the coast. Mountains (if they existed) would not have been nearly as high as they are currently. I do not think there was rain before the Fall and I think a strong case can be made for the lack of rain before the Flood.
The Flood brought massive geological change. The continents as they now appear are a result of breaking up either during the Flood or some time following. Sedimentary rocks and fossils they contain are diluvian phenomena. Mountain ranges are a result of this break up and they are much higher than previous ranges.
The release of water from the fountains of the deep was likely associated with significant heat and thus the waters would have been comparatively warmer. This would have led to significant evaporation. Water would have been released from the air in the form of rain and snow, but especially in areas where the air was significantly cooler (as it can hold less water), that is, at the poles where there was less sunlight warming, especially during the respective winters. Massive snow falls over the years would have led to accumulating ice, and cooler poles which may have intensified precipitation of water previously evaporated from the warmer equatorial seas. This process would have slowed as the equatorial seas cooled. The beginning of the ice-age would not be immediately following the Flood as time was needed for animals to migrate and populate various regions. That these animals were trapped in ice in such enormous numbers suggests a reasonably quick progression of the ice-age during at least part of its expansion.
Some current estimates of the ice-age have it commencing within a few centuries of the Flood and reaching a peak over ~2 centuries with an initial melt-back to near current levels over ~5 centuries*.
The initial postdiluvian climate was not in a state of equilibrium. The process of the waters cooling led to the ice-age. It is uncertain whether significant polar ice-caps would have formed had the water not been warm. Polar ice-caps are now present (due to the ice-age) and it is not certain whether they represent a potential equilibrium, or whether they will disappear over time. In other words, given our current global landscape, solar irradiation, and other climatic inputs, the earth may have more than one equilibrium state depending on initial conditions: with or without polar icecaps.
*Due to difficulties estimating variables for mathematical modelling, and establishing the models, I think that documentary evidence will be helpful in delineating this timeframe.