Legally speaking, the Satmar Rebbe did not say that it is absolutely forbidden for Jews to go to Eretz Yisroel. However, he did say that since there are many nisyonos and pitfalls for a Jew who goes there, it is almost never possible to take the responsibility of advising someone to go. In his words:

"There is a great halachic danger in living under the heretical government, for several reasons& there is no doubt that anyone who gives the slightest encouragement to the root of heresy, whether through money, honor or words, in any way, is worse than one who gives honor or money or encouragement to idolatry. A partial concession to the root of heresy is worse that a concession to idolatry. Those who live there have great difficulty being careful of this, and the tests are incredibly hard. Every person has many opportunities to commit this sin, whenever he needs some benefit from them, for everything is in the hands of the government, and people give them encouragement and praise in different ways, sometimes unwillingly and sometimes willingly. It is difficult to decide on such a subject where there are almost every day, and sometimes every minute, questions of sins where one must be killed rather than transgress. Who is the rabbi or leader in our generation who can rule on such severe questions? (Vayoel Moshe, Maamar Yishuv Eretz Yisroel, Siman 153)

He says that since heresy is worse than idolatry, and we know that it is forbidden to give even the slightest impression of believing in or supporting idolatry (and one must let himself be killed rather than do this), it is similarly forbidden to do or say anything that would give even the slightest impression of believing in or supporting the heretical Zionist state. Jews who live there encounter opportunities to commit this sin every day, and sometimes every minute of the day. Who then is authority who can take on his shoulders this responsibility of ruling on such a question?

He quotes the words of the Maharam Schick, who writes that if Chazal say that it is forbidden to do something physically dangerous, such as walking under a leaning wall, then certainly it is forbidden to go in a place where there is danger to the soul.

The Rebbe said that one may not visit the Kosel Hamaaravi, the Old City or any other areas conquered by the Zionists in 1967, because one might be influenced to feel some sort of gratitude to them for conquering it in violation of the Oaths. He wrote that even a good thing or a mitzvah should not be done if it was started by wicked people see Al Hageulah V'al Hatemurah, chapters 88-108 for these and more reasons. However he did not say this regarding the rest of Eretz Yisroel (see beginning of chapter 92 "shekavshu atah"), probably because Jews had access to these places before the state was founded and no one feels indebted to the Zionists for that. In a time such as ours when so many people visit these places and see nothing wrong with it, it would be unwise to subject oneself to this nisayon of going to study in Eretz Yisroel and refusing to visit them in accordance with the Rebbe's ruling.

So in short, halachically the Rebbe did not prohibit people from going to Eretz Yisroel, but he did strongly discourage it, even when done for learning Torah. He did permit it in individual cases when there was a very good reason. For example, he permitted Rabbi Moshe Aryeh Freund to return to Jerusalem after the 1967 war, since he was an influential and important figure in the Eidah Charedis. In 1946, the Rebbe himself had plans to stay there and strengthen the community in its fight against Zionism, and even when he went to America to escape the dangerous situation there in the years 1947-48, he at first planned to go back. These outstanding examples cannot serve as a precedent for all people and every case needs to be considered individually. Usually, whatever good reasons there are to go are outweighed by the dangers, both spiritual and physical.

The physical dangers of living in Eretz Yisroel have greatly increased since the Rebbe's time, and nowadays it is allowed to visit Eretz Yisroel only if the following two conditions are met: 1) you have concluded that it is not a dangerous place now, under Zionist rule; and 2) you feel it would not be a dangerous place if it came under Arab rule.

The first condition is because it is forbidden to go to a place of danger. This law is found in Taanis 20b, "A person should never go in a dangerous place and say, G-d will make a miracle for me. For perhaps G-d will not make a miracle for him, and even if He does, the cost of the miracle will be deducted from the person's merits."

The second condition is necessary because if you hold that the current situation is safe, but giving up the state would be dangerous, then by going there you will be putting yourself in a self-contradictory position. You oppose the state's existence but want it to exist at least temporarily while you are there.

But even if you fulfill the second condition, you cannot go unless you think it is safe right now. The reason is simple: even if you wish there were no danger, as long as there is danger you cannot go.

I hope this information answers your question.