Lady Dudley was walking home through the park to see all the trees that were blown down by that cyclone last year.
In Don Gifford's 1974 book, Notes for Joyce, it is explained that this refers to one of the most severe gales in Dublin's history and was compared at the time to that of 1839 (the night of the big wind). The gale caused great damage to property and particularly to trees in Phoenix Park. It is estimated that between 1000-3000 trees were uprooted in the park. In parts of the country it was reported that whole woods were leveled.
A cyclone that could bring down so many trees in Dublin would be seen as a catastrophic event today, and final proof of man made climate change / the end of the world. But we don't get storms that have this much force anymore, they are a thing of the past. Historic climatic events such as in 1839 and 1903 show that the climate, if anything, has actually improved in Ireland.
