There are a lot of people saying Russia won't want a military confrontation in winter. This is not true: For starters, attacking in winter gives Russia leverage over Europe because they can threaten to turn off the gas pipeline and leave Europe struggling to meet its needs for heating fuel. Second, frozen terrain is far from the worst when it comes to invading Ukraine---frozen soil is solid soil; it is wet, rainy soil that represents a problem. In fact, it is precisely the winter season that sees no rain in Ukraine. The ideal time to invade Ukraine is, strangely enough, about mid-February---assuming your troops are equipped for cold weather which, invariably, Russian troops would be.
Kiev seems to be more worried about the economic harm fear of a military invasion is doing than the prospect of an invasion itself: However, if I were Kiev, I would be trying to make the most use of that old Soviet equipment that I could even if doing so risked startling the populace more. I believe much of it could be salvaged to create a defensive line of hidden gun emplacements on the other side of the Dnieper---and that the fully operational ones could be hidden throughout the country with the idea of having them mobilize against the Russian forces after they have advanced beyond them while their most modern tanks carry out a more fighting retreat---with about half being kept in reserve beyond the Dnieper to deal with Soviet attempts to create a beachhead.
Of course, the problem of how to best use Ukrainian airpower is a difficult one. That said, we could meaningfully supplement it, the US has about 21 Mig-29's in our inventory that we bought from Moldova in order to keep them out of Iran's hands. We could easily sell, let's say, 18 of these to Ukraine and meaningfully bolster their air force (obviously, we have to keep some for threat assessment, training, etc.) Going from 125 planes to 143 is a meaningful increase---and as their pilots are already trained on the Mig-29, these planes could be immediately integrated. Also, if India could be induced to sell Ukraine some of its Migs and Sukhoi's in exchange for access to US planes, this could be a double win---as it helps Ukraine and places pressure on China. Even if we are unwilling to sell them the F-35, the F-15 FX and the F-15 S (which did not find a buyer but deserves to) models could be very valuable additions to their air force's capacity. We could also attempt to upgrade Ukraine's Sam systems. If India is not willing to play along, Poland might be willing to donate its Mig-29s in a similar deal.
By saving most of their airpower to oppose the crossing of the Dnieper (unless their fighting retreat goes esp. well), the Ukrainians can use the fact that they will have a higher sortie rate and the Russians a lower one as an airpower multiplier. However, if they attempt to oppose the Russians with their airpower too early in the conflict, namely, closer to the Russian border, the Russians will not be at a sortie disadvantage. The reason the Russians will take more time between sorties is that they will have to fly from their bases in Russia over all the Ukrainian territory they have taken, while the Ukrainians will only have to fly from their bases on the other side of the Dnieper to wherever the Russian front line will be.
The Ukrainians also need to hide weapons and supply caches throughout the country—esp. those eastern portions which are not populated with Russian partisans—while ensuring that they remain accessible to their own forces and hidden from the Russians. Guerilla activity should make organizing the crossing of the Dnieper more difficult and allow the Ukrainians to impose upon the Russians a cost that threatens Putin’s popularity at home much as the Afghans did in the 1980’s. It goes without saying that they should attempt to hand out as much “guerilla equipment” including rifles as they possibly can. They should also immediately call up their reserves and begin training—even a week or two of training can make a major difference regarding a military force’s combat readiness.
Ukrainians should also immediately begin to manufacture tank obstacles by tying together railroad track (think of the obstacles used to prevent landings at Normandy) and to place them in locales that will hinder the Russian armored advance (though without hindering Ukraine’s own forces). They need to destroy all the bridges leading into Ukraine as well as all the connections between the Ukrainian railway network and the Russian and Belarussian ones.
The secret to defending Ukraine is to bleed the Russians as much as possible at every phase while minimizing loss of your own military resources—even at the cost of territory at least until the Russians reach the Dnieper. They may not have much success in defending the East, but they must hold the West and they must extract a very high price for taking Kiev.