They had good reasons to evacuate: There were riots due to famine and war weariness; on 30.12.1916 (17.XII) a conspiracy of nobles killed Rasputin, whose "revelations" had had a substantial influence on the course of the war. The army was on the brink of mutiny; on 27.2.2017 (14.II) army officers in Petrograd joined demonstrations against the government.

On 2.3.1917, the Swedish government endorsed a transfer across the ice of the imperial train "se trouvant actuellement à Copenhague". Sweden apparently did not want to get dragged into the war by violating its neutrality, so the government insisted on removing the rail connection for security reasons as soon as the train had passed; on 10.3.2017 it explicitly denied rumours of freight transport across the ice. On 8.3.2017 the sealed train (9 bogie cars, one luggage car) was placed under military guard at Morjärv (around 90km from Haparanda), ready for transfer on Sunday, but on 10.3.1917 the Finnish side reported that they would not be ready before Monday noon (12.3.2017) or Tuesday.

Meanwhile, on Saturday 3.3.1917 (18.III), strikes and demonstrations began in Petrograd. In the next days the supplies of bread and fuel were running low, heavy showstorms had stranded many freight trains; the government started rationing flour and bread. On Thursday 8.3.1917 (23.II) the strikes developed into riots and a full-blown upheaval. On 9.3.1917 (24.II) around 200,000 protesters demanded the Tsar's abdication; by Saturday 10.3.2017 (25.II) some 250,000 people were on strike. On Sunday 11.3.1917 (26.II) Tsar Nicholai ordered the army to suppress the riots, one regiment mutinied, in the evening he suspended the Duma. On Monday 12.3.1917 (27.II) the Council of Ministers resigned, the mutiny spread to the bulk of the garrison, 40,000 rifles were dispersed among the workers, the signs of the Tsarist regime were torn down. In the following days, the units guarding the imperial palace at Tsarskoye Selo either joined the mutineers in Petrograd or declared their neutrality.

On Tuesday 13.3.1917 (28.II) Dagmar's imperial train was transferred across the ice to Finland. Early the same day, Tsar Nicholai had left Mogilev to return to Petrograd, but his train was stopped in at Malaya Vishera (160km before Petrograd) and sent back towards Pskov, arriving 14.3.1917 (1.III) in the evening. Thursday morning 15.3.1917 (2.III), in the imperial train in Pskov (the train that later was exhibited in Peterhof museum and destroyed during WWII) and in the presence of the envoys of the Duma, Tsar Nicholai signed two abdications, the first in favour of his son, the second in favour of his brother, Grand Duke Michael Alexandrovich. The next day, Friday 16.3.2017 (3.III), his brother declined the crown; the Provisional Government declared itself governing body. The rest is history.

On Tuesday 29.4.1917 (16.IV), Lenin arrived by train in Petrograd from Zürich, taking the same route via Haparanda as the imperial train. The Russian history hinges on trains!

One open question is, are the imperial carriages that were transported across the ice on 13.3. (28.II) identical to those used for signing the abdication in Pskov on the morning of 15.3. (2.III)? I find it unlikely; it is a distance of over 1100km by rail, passing through Petrograd which was controlled by the revolutionaries.

"By 1902, the train consisted of ten carriages: a sleeping-car for the Emperor and Empress, a saloon car, a kitchen, a dining car, carriages intended for the grand dukes and other family, the children's car, cars for the Emperor's retinue, as well as cars for railway servicemen, servants, luggage and workshops. The final and eleventh car, a fully dedicated chapel, was consecrated in 1899."
http://www.theromanovfamily.com/romanov-family-inside-imperial-train/

This is obviously wrong, 1899 is before 1902. But it suggests that there existed at least eleven imperial cars, including a chapel. The chapel might well have accompanied Maria Feodorovna (née Dagmar) on her travel to Denmark, as there is no Russian Orthodox chapel at "Bernstorff slot", the summer residence of the Danish Royal Family. (The Grand Duke of Hesse in Darmstadt could offer his visitors a consecrated Russian church; the King of Prussia's summer residence in Bad Homburg had both a Russian chapel and an English Church!)

If there existed "at least eleven imperial cars", it would (almost) account for three cars for Nicholai plus nine cars for Dagmar (plus a non-imperial luggage van). This leaves the question, what happened to Dagmar's train? Did it ever leave Finland?