@Amrando
What you say is correct for GSM, which indeed can handle handovers only up to 250km/h (GSM900) or 130 km/h (GSM1800), which is due to the so-called "timing advance": On GSM networks up to 8 terminals (= handsets) share the same frequency. In order to avoid interference each handset may only "talk" and "listen" during a time frame of 577μs, which is assigned to each terminal by the network. So practically each phone has just a small so-called timeslot of 577μs every 4616μs during which it may communicate. Now since the signal from a terminal next to the cell tower reaches the cell tower faster than the signal from a more distant terminal their communication would overlap and cause interference. That's why you need to consider the distance respectively the signal transit time between the terminal and the cell tower and adjust the timing so all signals arrive just in time to match the assigned timeslot. A more distant phone, whose signal has to travel longer hence would reach the celltower delayed and so miss it's timeslot, has to send it's signal a bit earlier in order to offset the delay of the longer transit time. This adjustment is called "timing advance" and the problem is simply, that if you travel too fast and approach the cell tower with high speeds you need to adjust timing advance faster than the GSM standard allows.
Btw the limited ability of timing advance also limits the range of GSM900 to 35km (allthough some network equipment manufacturers have "extended range" solutions, which double the range by recuding the number of timeslots to 4 at the expense of capacity halving, so only 4 terminals can share the same frequency).
Radio technologies which are based on all terminals sharing the same frequency by using it only during assigned timeslots are called Timing Divison Multiple Access (TDMA).
3G/UMTS in contrast is a Code Division Multiple Access (CDMA) technology where all terminals listen and talk simultaneously and the signal is later being subtracted out by a spreading code. This is a bit more complicated than TDMA and thus a detailed explanation would go beyond the scope of this discussion. However as a result UMTS can handle handovers up to 500km/h, so it would generally work even on high speed trains.
In the field however the main problem is the shielding from the metal frame of the train cars and additionally the metall coated windows on modern trains, which causes high attenuation (= weakening of the signal). Further those high-speed tracks lead often apart from populated areas, which have inferior cell coverage and then there are a lot of tunnels, which provide even worse to none reception.
Lastly at least in Germany we have the problem of UMTS networks only operating at 2100 MHz, which is a comparably high frequency, which has a way shorter range than our GSM networks, which operate at 900 and 1800 MHz and has worse signal dispersion properties, which basicly means signals at 2100 MHz are impacted even more by the attenuation of the metal frame and coated windows.
In other European countries they have UMTS also running at 900 MHz, which improves user experience significantly. The same applies for America, where AT&T, Rogers/Fido and Bell/Telus run UMTS at 850 MHz, while T-Mobile USA and Wind Mobile, Mobilicity, Videotron use the AWS band (1700MHz for uplink and 2100MHz for downlink) suffer from the physical disadvantages of the high frequencies they were awarded.